20 ! 2 questions
segment ab falls on line 2x − 4y = 8. segment cd falls on line 4x + 2y = 8. what is true about segments ab and cd?
they are perpendicular because they have the same slope of −2.
they are perpendicular because they have slopes that are opposite reciprocals of −2 and one half.
they are coincident lines because they have the same slope and the same y-intercept.
they are coincident lines because they have the same slope and a different y-intercept.
annie is creating a stencil for her artwork using a coordinate plane. the beginning of the left edge of the stencil falls at (1, −1). she wants to align an important detail on the left edge of her stencil at (3, 0). she knows this is 1: 3 of the way to where she wants the end of the stencil. where is the end of the stencil located?
(1.5, −0.75)
(2.5, −0.25)
(6, 2)
(9, 3)

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)

20

step-by-step explanation: