Question

A, B, C, and D have the coordinates (-8,1), (-2,4), (-3,-1), and (-6,5), respectively. Which sentence about the points is true? A.) A, B, C, and D lie on the same line. B.) AB and CD are perpendicular lines. C.) AB and CD are parallel lines. D.) AB and CD are intersecting lines but are not perpendicular. E.) AC and BD are parallel lines. PLEASE HELP ASAP!!! ​

Answer 1

B.) AB and CD are perpendicular lines

Explanation:

we have

`A(-8,1),B(-2,4),C(-3,-1),D(-6,5)`

Verify each statement

A.) A, B, C, and D lie on the same line

The statement is False

To better understand the question plot the points

using a graphing tool

see the attached figure

therefore

The points A, B, C, and D not lie on the same line

B.) AB and CD are perpendicular lines

The statement is True

Because

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal of each other (the product is equal to -1)

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

Find the slope AB

`A(-8,1), B(-2,4)`

Substitute the values

`m=(4-1)/(-2+8)`

`m=(3)/(6)`

`m=(1)/(2)`

Find the slope CD

`C(-3,-1),D(-6,5)`

Substitute the values

`m=(5+1)/(-6+3)`

`m=(6)/(-3)`

`m=-2`

Find the product of the slopes

`(1)/(2)*(-2)=-1`

therefore

The lines AB and CD are perpendicular

C.) AB and CD are parallel lines.

The statement is False

Because

Lines AB and CD are perpendicular lines (see the part B)

D.) AB and CD are intersecting lines but are not perpendicular

The statement is false

Because

Line AB and line CD are intersecting perpendicular lines (see the part B)

E.) AC and BD are parallel lines

The statement is false

Because

we know that

If two lines are parallel, then their slopes are the same

Find the slope AC

`A(-8,1),C(-3,-1)`

Substitute the values

`m=(-1-1)/(-3+8)`

`m=(-2)/(5)`

`m=-(2)/(5)`

Find the slope BD

`B(-2,4),D(-6,5)`

Substitute the values

`m=(5-4)/(-6+2)`

`m=(1)/(-4)`

`m=-(1)/(4)`

Compare the slopes

`-(2)/(5)\\eq-(1)/(4)`

therefore

AC and BD are not parallel lines