Question

Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.

Answer 1

Lines a and b are parallel

Lines a and c are perpendicular

Lines d and c are perpendicular

Explanation:

we know that

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

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

Part 1) Find the slope of Line a

we have the points

(-3,4) and (3,6)

substitute in the formula

`m=(6-4)/(3+3)`

`m=(2)/(6)`

simplify

`m_a=(1)/(3)`

Part 2) Find the slope of Line b

we have the points

(-10,-3) and (-8,3)

substitute in the formula

`m=(3+3)/(-8+10)`

`m=(6)/(2)`

`m_b=3`

Part 3) Find the slope of Line c

we have the points

(0,5) and (3,-4)

substitute in the formula

`m=(-4-5)/(3-0)`

`m=(-9)/(3)`

`m_c=-3`

Part 4) Find the slope of Line d

we have the points

(4,-7) and (13,-4)

substitute in the formula

`m=(-4+7)/(13-4)`

`m=(3)/(9)`

simplify

`m_d=(1)/(3)`

Part 5) Compare the slopes

Remember that

If two lines are parallel then their slopes are the same

If two lines are perpendicular then their slopes are opposite reciprocal

we have

`m_a=(1)/(3)`

`m_b=3`

`m_c=-3`

`m_d=(1)/(3)`

therefore

Lines a and b are parallel (slopes are equal)

Lines a and c are perpendicular (slopes are opposite reciprocal)

Lines d and c are perpendicular (slopes are opposite reciprocal)