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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)

Determine whether PQ and UV are parallel, perpendicular, or neither. 1.P(-3,-2), Q-example-1

2 Answers

7 votes

Answer:

9

Explanation:

User P Basak
by
8.2k points
6 votes

Answer:

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

User Nick Garvey
by
8.4k points

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