Question

Determine whether PQ and UV are parallel,

perpendicular, or neither.
1.P(-3,-2), Q(9,1), U(3,6), V(5,-2)
2.P(-10,7), Q(2,1), U(4,0), V(6,1)
3.P(1,1), Q(9,8), U(-6,1), V(2,8)
4.P(-4,0), Q(0,3), U(-4,-3), V(8,6)
5.P(-9,2), Q(0,1), U(-1,8), V(-2,-1)

Answer 1

9

Explanation:

Answer 2

The answer is below

Explanation:

The slope of a line (m) is given by:

`m=(y_2-y_1)/(x_2-x_1)`

Two lines are parallel if they have the same slope and perpendicular if the product of their slope is -1.

1)

`Slope\ of\ PQ=(1-(-2))/(9-(-3))=(1)/(4) \\\\Slope\ of\ UV=(-2-6)/(5-3)=-4`

Since the product of their slope is -1, they are perpendicular

2)

`Slope\ of\ PQ=(1-7)/(2-(-10))=-(1)/(2) \\\\Slope\ of\ UV=(1-0)/(6-4)=(1)/(2)`

Since the slope is not the same or product of their slope is not -1, they are neither parallel or perpendicular

3)

`Slope\ of\ PQ=(8-1)/(9-1)=(7)/(8) \\\\Slope\ of\ UV=(8-1)/(2-(-6))=(7)/(8)`

Since the slopes are the same, they are parallel

4)

`Slope\ of\ PQ=(3-0)/(9-(-4))=(3)/(4) \\\\Slope\ of\ UV=(6-(-3))/(8-(-4))=(3)/(4)`

Since the slopes are the same, they are parallel

5)

`Slope\ of\ PQ=(1-2)/(0-(-9))=-(1)/(9) \\\\Slope\ of\ UV=(-1-8)/(-2-(-1))=9`

Since the product of their slope is -1, they are perpendicular