Question

Endpoints of segment MN have coordinates (0, −3), (−2, −4). Endpoints of segment AB have coordinates (2, 5), (4, k).

Answer 1

Answer:

The value of k is 6

Step-by-step explanation:

we know that

If two segments are parallel, then their slopes are the same

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope MN

we have

M(0, −3), N(−2, −4)

substitute

$m=\frac{-4+3}{-2-0}$

$m=\frac{-1}{-2}$

$m=0.5$

step 2

Find the slope AB

A(2, 5), B(4, k)

substitute in the formula

$m=\frac{k-5}{4-2}$

$m=\frac{k-5}{2}$

Remember that the slopes MN and AB must be equal

$0.5=\frac{k-5}{2}$

Solve for k

$1=k-5$

$k=1+5=6$

therefore

The value of k is 6