Lessons on Coordinate geometry for WASSCE, JAMB and NECO candidates.

1. Worked
Examples
Multiple
Choice
Practice
Questions
Lesson
Notes EXIT

2. i. Distances, d = 𝑥1 − 𝑥2
2 + 𝑦1 − 𝑦2
2
AB = 𝑥1 − 𝑥2
2 + 𝑦1 − 𝑦2
2
4
−5
AB = 1 + 2 2 + 3 + 1 2
AB = 32 + 42
ii. AB = 9 + 16 = 25 = 5 𝑢𝑛𝑖𝑡𝑠
𝐵𝐶 =
2
3𝑚
−
−2
−1
=
4
3𝑚 + 1
⇒
4
−5
=
4
3𝑚 + 1
⇒ 3𝑚 + 1 = −5
⇒ 𝑚 = −2
Given that A(1,3), B(-2,-1) and C(2,3m) where
m is a constant, find
|AB|;
The value of m if 𝐵𝐶 =
4
−5
𝑊𝐴𝑆𝑆𝐶𝐸 𝐽𝑈𝐿𝑌, 2007.

3. Gradient =
𝑦2 − 𝑦1
𝑥2− 𝑥1
=
4−0
1−3
= −2
A straight line passes through the points (1,
4) and (3, 0). Find the gradient of the line.
𝑊𝐴𝑆𝑆𝐶𝐸 𝐽𝑈𝐿𝑌, 2009.

4. Find the distance between these points, A ( 3, 5)
and B(2, 6).
A . 2 units
B . 146 units
C . 1 unit
D √6 units
E. 2 units
EXIT
MCQ

5. Find b given that A(3, -2) and B(b, 1) are 13
units apart.
B .1 or 5
A . 5
C −5 𝑜𝑟 − 1
D .−5 𝑜𝑟 1
E . 1
EXIT
MCQ

6. Find the coordinate of the midpoint of A(-1, 3) and
B(4,7)
B. (1
1
2
, 5)
A .(3
1
2
, 5)
C .( − 1
1
2
, 5)
D .(2
1
2
, 5)°
•
•°
E . ( − 2
1
, 5)
EXIT
MCQ

7. If A is (𝑥1, 𝑥2) 𝑎𝑛𝑑 𝐵 𝑦1, 𝑦2 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 𝐴𝐵 𝑖𝑠
E .
𝑦1− 𝑦2
𝑥1− 𝑥2
A .
𝑥1− 𝑥2
𝑦1− 𝑦2
D .
𝑥1− 𝑥2
𝑦2− 𝑦1
B .
𝑥2− 𝑥1
𝑦2− 𝑦1
C .
𝑥1∓ 𝑥2
𝑦1− 𝑦2
EXIT
MCQ

8. Find the slope of the the line through (3,2) and (6,4)
D.
2
3
A .−
2
3
E.
1
3
B.
3
2
C .−
3
2
EXIT
MCQ

9. Find t given that M(t, 7) and N(-1,7) such that
the midpoint of MN is −
5
2
, −2
C. 4
A .2
D .5
B .3
E .6 EXIT
MCQ

10. Find the equation of a straight line with gradient, 2 and passes
through (0,2).
A . 2𝑦 = 4𝑥 + 4
C . 2𝑦 = 𝑥 + 1
D . 2𝑥 + 2𝑦 = 1
B . y = 2𝑥 − 2
E . 𝑦 = 2𝑥
EXIT
MCQ

11. The 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 of a line is (0, −9). Find the equation of the
straight line if it’s gradient −1.
B . x + 𝑦 = −9
A .𝑦 = −𝑥 + 9
D .𝑥 + 𝑦 = 9
C . 𝑥 − 𝑦 = 9
E .𝑦 = −9𝑥 − 1 EXIT
MCQ

12. The equation of a straight line is given by 𝑥 = 9 − 𝑦. What is
the 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑜𝑓 the line?
D .9
A .−9
B . 1
C .−1
E. 0
EXIT
MCQ

13. The line 𝑦 =
3
4
𝑥 + 𝐾 passes through the origin. Find
the value of k.
D . 𝑘 = 0
A. 𝑘 = −
4
3
C .𝑘 = −
3
4
B .𝑘 = 1
C . 𝑘 = −1

14. EXIT
MCQ
Distance between two points

15. EXIT
MCQ
Midpoint of a straight-line

16. EXIT
MCQ
Gradient of a straight-line
The slope is the change in y divided by the
change in x

17. EXIT
MCQ
Gradient of a straight-line
When a straight line makes an angle of 𝜃° in the positive direction of the
x-axis, then the tangent of 𝜃° gives the slope of the line.

18. EXIT
MCQ
Perpendicular & Parallel lines
If two lines are parallel then, the they have the same
gradients. If the two lines are perpendicular then the
product of their gradient is −1.

19. EXIT
MCQ
Equation of a straight-line(Two points)

20. Equation of a straight-line(Point-Slope form)