powerpoint

2. To determine the distance between any two points on a real
number line. We get the absolute value of the difference of their
coordinates.
Steps Solution
1. Determine the coordinates of Q and R. Q = -6 and R = -3
2. Find the absolute value of the difference of
the coordinates of Q and R.
QR = |-6 – (-3)| = |-3| = 3

3. Example 1. Find the length of segment XY.
Steps Solution
1. Find the x coordinates of
X and Y.
A = (
1
𝑥
, -3) and Y = (
5
𝑥
, -3)
2. Find the distance
between X and Y.
The x coordinate of X
the x coordinate of Y.
XY = 5 – 1 = 4
or
= |1 – 5 |
= |-4 | = 4
Therefore the length of segment XY is the distance between X and Y which is
4 units.

4. Example 2. Find the length of segment ST.
Steps Solution
1. Find the coordinates of S
and T.
S = (-4,
6
𝑦
) and Y = (-4,
1
𝑦
)
2. Find the distance
S and T.
The x coordinate of S minus
the x coordinate of T.
XY = 6 – 1 = 5
or
= |1 – 6 |
= |-5 | = 5
Therefore the length of segment ST is the distance between S and T which is
5 units.

5. Example 3. Find the length of segment AB.
Steps Solution
1. Find the coordinates of A
and B.
A = (
−3
𝑥
, 2) and B = (
1
𝑥
, 2)
2. Find the distance
between A and B.
The x coordinate of A
minus the x coordinate of
B.
AB = 1 – (-3) = 4
or
= |(-3) – 1 |
= |-4 | = 4
Therefore the length of segment AB is the distance between A and B which is 4
units.

6. Example 4. Find the length of segment CD.
Steps Solution
1. Find the coordinates of
C and D.
C = (3,
1
𝑦
) and Y = (3,
−4
𝑦
)
2. Find the distance
between S and T.
The x coordinate of S
minus the x coordinate of
T.
CD = 1 – (-4) = 5
or
= |-4 – 1 |
= |-5 | = 5
Therefore the length of segment CD is the distance between C and D
which is 5 units.

8. Example 5. Find the length of segment QP
.
Steps Solution
1. Let P = (2, 2) and
R = (7, 2)
Q = (7, 7)
Find the distance of x
coordinates
The x coordinates of R
minus and P.
PR = 7 - 2 = 5
2. Find the distance
between y coordinates.
The y coordinates of Q
minus R.
QR = 7 – 2 = 5

9. Steps Solution
3. Find the distance between Q and P
.
Take the square root of the sum of the
square of the length of PR and the
square of the length of QR.
QP = 𝑃𝑅 2 + 𝑄𝑅 2
QP = 5 2 + 5 2
= 25 + 25
= 50
= 5 𝟐

10. Distance Formula
The distance between two points A(x1, y1) and B(x2, y2) on
the coordinate plane is:
or

11. Let’s Apply:
1. Let A = (-3, -1), B = (2, -1), and C = (2, 3).
Find AB, BC, and AC
Solution:
AB = x2 – x1
= 2 – (-3)
= 2 + 3 = 5
BC = y2 – y1
= 3 – (-1)
= 3 + 1 = 4

12. AC = 𝑥2 − 𝑥1
2 + 𝑦2 − 𝑦1
2
AC = 2 − (−3) 2 + 3 − (−1) 2
AC = 2 + 3 2 + 3 + 1 2
= 5 2 + 4 2
= 25 + 16
= 41