LINE SEGMENTS AND DISTANCE

The numbers given are the coordinates of two points on a number line. State the distance between the points.

Problem 1 :

-3 and 5 _____

Solution :

x₁ = -3 and x₂ = 5

d = x₂ - x₁

= 5 - (-3)

= 5 + 3

d = 8

So, the distance between the points -3 and 5 is 8. 

Problem 2 :

-15 and -8 _____

Solution :

x₁ = -15 and x₂ = -8

d = x₂ - x₁

= -8 - (-15)

= -8 + 15

d = 7

So, the distance between the points -15 and -8 is 7. 

Problem 3 :

-1 and 9 _____

Solution :

x₁ = -1 and x₂ = 9

d = x₂ - x₁

= 9 - (-1)

= 9 + 1

d = 10

So, the distance between the points -1 and 9 is 10. 

Problem 4 :

-11 and -27 _____

Solution :

x₁ = -11 and x₂ = -27

d = x₂ - x₁

= -27 - (-11)

= -27 + 11

d = -16

So, the distance between the points -11 and -27 is -16. 

Name each of the following.

Problem 5 :

The point on GC whose distance from G is 3 _____

Solution :

Distance from G is 3 and the point is D.

Problem 6 :

Two points whose distance from I is 4 _____

Solution :

So, two points are E and M.

Problem 7 :

The midpoint of DJ _____

Solution :

The midpoint of DJ is G

Problem 8 :

The coordinate of the midpoint of CG ____

Solution :

The coordinate of the midpoint of CG is -3.

Problem 9 :

The ray opposite to DF ____

Solution :

The ray opposite to DF is CD.

Problem 10 :

A segment congruent to DL _____

Solution :

Congruent segments is CM, EK and FJ ....

R is the midpoint of PS. Find the value of x.

Problem 11 :

PR = 3x + 2, RS = 5x - 4 ____

Solution :

PR = RS

3x + 2 = 5x - 4

2 + 4 = 5x - 3x

6 = 2x

x = 6/2

x = 3

So, the value of x is 3.

Problem 12 :

PR = 6x - 1, PS = 8x _____

Solution :

PR = 6x - 1

PS = 8x

PR = PS

6x - 1 = 8x

6x - 8x = 1

-2x = 1

x = -1/2

So, the value of x is -1/2.