Question

Given A(2, 5), B(6, –11), and C(3, 10), which coordinate will make parallel to ?

D(11, 4)


D(–1, 9)


D(9, –1)


D(2, 14)

Answer 1

The coordinate D that will make AB parallel to CD is (2, 14)

For two lines to be parallel to each other, the slopes of the line must be equal.

Given the coordinates A(2, 5), B(6, –11), and C(3, 10), D(x, y).

We first need to get the slope AB and CD

For the coordinate A(2, 5) and B(6, –11)

$m_{AB} = \frac{-11-5}{6-2}\\m_{AB}=\frac{-16}{4} \\m_{AB} =-4$

For the coordinate C(3, 10) and D(x, y)

$m_{CD} = \frac{y-10}{x-3}$

Since the slope is the same:

$\frac{y-10}{x-3} =-4\\-4(x-3) = y-10\\-4x+12=y-10$

On checking the value of x is 2 and y is 14.

Hence the coordinate D that will make AB parallel to CD is (2, 14)

Learn more here: https://brainly.com/question/16949303