Question

Consider two parallel line segments.

Part A: Find the slope of segment CD with endpoints C(−7, −2) and D(−4, 2). Show your work. (2 points)

Part B: What is the value of y so that segment AB with endpoints A(4, y) and B(7, 4) is parallel to segment CD question mark Show your work. (2 points)

Answer 1

see explanation

Explanation:

A

Calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = C(- 7, - 2) and (x₂, y₂ ) = D(- 4, 2)

m =
`(2+2)/(-4+7)` =
`(4)/(3)`

--------------------------------------

B

Parallel lines have equal slopes.

Calculate the slope of AB and equate to the slope of CD

(x₁, y₁ ) = A(4, y) and (x₂, y₂ ) = B(7, 4)

m =
`(4-y)/(7-4)`, that is

=
`(4-y)/(3)` =
`(4)/(3)` ( cross- multiply )

3(4 - y) = 12 ( divide both sides by 3 )

4 - y = 4 ( subtract 4 from both sides )

- y = 0 ⇒ y = 0