This one is a problem solving question in coordinate geometry. The questions tests your understanding to determine the x and y intercept of a line and find the area of a triangle formed between the line and the coordinate axes. What is the area of the triangle formed by the coordinate axes and the line L whose equation is 2x - 3y = 6? A) 6 B) 12 C) √(13) D) 3 E) 7.5

1. GMAT QUANTITATIVE REASONING
COORDINATE GEOMETRY
PROBLEM SOLVING
Diagnostic Test

2. Question
What is the area of the triangle formed by the coordinate
axes and the line L whose equation is 2x - 3y = 6?
A. 6
B. 12
C. 13
D. 3
E. 7.5

3. Step 1
What kind of a triangle is formed?

4. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6

5. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
The coordinate axes (x and y axes)
form sides of the triangle.
The triangle is a right triangle.

6. Step 2
Plot the line on the x-y plane; determine
sides of the triangle; compute area

7. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Steps to compute area of the triangle

8. Compute x and y
intercepts using the
equation of the line.
x & y intercepts
01
What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Steps to compute area of the triangle

9. Compute x and y
intercepts using the
equation of the line.
Determine sides of
the triangle from x
and y intercepts
x & y intercepts Sides of triangle
01
02
What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Steps to compute area of the triangle

10. Compute x and y
intercepts using the
equation of the line.
Determine sides of
the triangle from x
and y intercepts
Using data on sides,
compute area of
triangle
x & y intercepts Sides of triangle Find area
01
02
03
What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Steps to compute area of the triangle

11. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. Equation of the line is 2x – 3y = 6
Step 01 : Compute x and y intercepts

12. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. Equation of the line is 2x – 3y = 6
x-intercept is the point where the
line meets the x-axis. At that point,
the y coordinate is ‘0’ (zero)
Step 01 : Compute x and y intercepts

13. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. Equation of the line is 2x – 3y = 6
x-intercept is the point where the
line meets the x-axis. At that point,
the y coordinate is ‘0’ (zero)
Step 01 : Compute x and y intercepts
To determine x-intercept of a line, substitute y =
0 in the equation of the line.

14. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. Equation of the line is 2x – 3y = 6
x-intercept is the point where the
line meets the x-axis. At that point,
the y coordinate is ‘0’ (zero)
Step 01 : Compute x and y intercepts
To determine x-intercept of a line, substitute y =
0 in the equation of the line.
2x – 3(0) = 6 or x = 3. x-intercept of the line is 3

15. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. Equation of the line is 2x – 3y = 6
x-intercept is the point where the
line meets the x-axis. At that point,
the y coordinate is ‘0’ (zero)
Step 01 : Compute x and y intercepts
To determine x-intercept of a line, substitute y =
0 in the equation of the line.
2x – 3(0) = 6 or x = 3. x-intercept of the line is 3
y-intercept is the point where the
line meets the y-axis. At that point,
the x coordinate is ‘0’ (zero)

16. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. Equation of the line is 2x – 3y = 6
x-intercept is the point where the
line meets the x-axis. At that point,
the y coordinate is ‘0’ (zero)
Step 01 : Compute x and y intercepts
To determine x-intercept of a line, substitute y =
0 in the equation of the line.
2x – 3(0) = 6 or x = 3. x-intercept of the line is 3
y-intercept is the point where the
line meets the y-axis. At that point,
the x coordinate is ‘0’ (zero)
To determine y-intercept of a line, substitute x =
0 in the equation of the line.

17. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. Equation of the line is 2x – 3y = 6
x-intercept is the point where the
line meets the x-axis. At that point,
the y coordinate is ‘0’ (zero)
Step 01 : Compute x and y intercepts
To determine x-intercept of a line, substitute y =
0 in the equation of the line.
2x – 3(0) = 6 or x = 3. x-intercept of the line is 3
y-intercept is the point where the
line meets the y-axis. At that point,
the x coordinate is ‘0’ (zero)
To determine y-intercept of a line, substitute x =
0 in the equation of the line.
2(0) – 3y = 6 or y = -2. y-intercept of the line is -2

18. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle

19. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
Join the x and y intercepts to plot the line.

20. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
(3, 0)
Join the x and y intercepts to plot the line.

21. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
(3, 0)
(0, -2)
Join the x and y intercepts to plot the line.

22. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
(3, 0)
(0, -2)
Join the x and y intercepts to plot the line.

23. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
(3, 0)
(0, -2)
Join the x and y intercepts to plot the line.
OAB is the triangle whose area has to be determined.
O
A
B

24. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
(3, 0)
(0, -2)
Join the x and y intercepts to plot the line.
OAB is the triangle whose area has to be determined.
O
A
B
OA, one of the sides of the right triangle is the x intercept of the line = 3 units

25. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
(3, 0)
(0, -2)
Join the x and y intercepts to plot the line.
OAB is the triangle whose area has to be determined.
O
A
B
OB, another side of the triangle is the y intercept of the line = 2 units
OA, one of the sides of the right triangle is the x intercept of the line = 3 units

26. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
(3, 0)
(0, -2)
Join the x and y intercepts to plot the line.
OAB is the triangle whose area has to be determined.
O
A
B
OB, another side of the triangle is the y intercept of the line = 2 units
Step 03 : Compute the area
OA, one of the sides of the right triangle is the x intercept of the line = 3 units

27. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
(3, 0)
(0, -2)
Join the x and y intercepts to plot the line.
OAB is the triangle whose area has to be determined.
O
A
B
OB, another side of the triangle is the y intercept of the line = 2 units
Step 03 : Compute the area
Triangle OAB is a right triangle and its perpendicular sides measure 2 and 3 units.
OA, one of the sides of the right triangle is the x intercept of the line = 3 units

28. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
(3, 0)
(0, -2)
Join the x and y intercepts to plot the line.
OAB is the triangle whose area has to be determined.
O
A
B
OB, another side of the triangle is the y intercept of the line = 2 units
Step 03 : Compute the area
Triangle OAB is a right triangle and its perpendicular sides measure 2 and 3 units.
Area =
1
2
× b × h =
1
2
× 3 × 2 = 3 units
OA, one of the sides of the right triangle is the x intercept of the line = 3 units

29. What is the area of the triangle?
Triangle is formed by the coordinate axes and the line 2x - 3y = 6
02 Compute area of the triangle. x intercept of line 3 and y intercept -2
Step 02 : Determine sides of triangle
(3, 0)
(0, -2)
Join the x and y intercepts to plot the line.
OAB is the triangle whose area has to be determined.
O
A
B
OB, another side of the triangle is the y intercept of the line = 2 units
Step 03 : Compute the area
Triangle OAB is a right triangle and its perpendicular sides measure 2 and 3 units.
Area =
1
2
× b × h =
1
2
× 3 × 2 = 3 units Choice D.
OA, one of the sides of the right triangle is the x intercept of the line = 3 units

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