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Step-by-step explanation:

Part 1) They are perpendicular because they have slopes that are opposite reciprocals of −2 and one half.

Part 2) The coordinates of the end of the stencil are (9,3)

Step-by-step explanation:

Part 1)

step 1

Find the slope of segment AB

we have

Segment AB falls on line

> isolate the variable y

Divide by 4 both sides

so

The slope of segment AB is m=1/2

step 2

Find the slope of segment CD

we have

Segment CD falls on line

> isolate the variable y

Divide by 2 both sides

so

The slope of segment CD is m=-2

step 3

Compare the slopes

mAB=1/2

mCD=-2

Remember that

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

(1/2) and -2 are opposite reciprocal

therefore

Segment AB and segment CD are perpendicular

Part 2)  

Let

A(1,-1) and B(3,0)

Find the x-distance between point A and B

dx=(3-1)=2 units

we know that

The point (3,0) s 1:3 of the way to where she wants the end of the stencil

Multiply by 3 the x-distance between point A and B

3(2)=6 units

The x-coordinate of the end of the stencil will be 6 units plus the x-coordinate point (3,0)

x-coordinate=6+3=9

Find the y-distance between point A and B

dy=(0+1)=1 units

we know that

The point (3,0) s 1:3 of the way to where she wants the end of the stencil

Multiply by 3 the y-distance between point A and B

3(1)=3 units

The y-coordinate of the end of the stencil will be 3 units plus the y-coordinate point (3,0)

y-coordinate=3+0=3

therefore

The coordinates of the end of the stencil are (9,3)