Question

AB has endpoints of A(2,-8) and B (-4,12). What are the coordinates of 3/4 of the way to B?

a. (-2,6)
b. (-3,9)
c. (-3,6)
d. (-2,9)

Answer 1

The coordinates that are 3/4 of the way to point B are (-2.25, 9.5).

Step-by-step explanation:

To find the coordinates that are 3/4 of the way to point B, we need to determine the midpoint between points A and B, and then find the coordinates that are 3/4 of the distance from the midpoint to point B.

Step 1: Find the midpoint of points A and B.

Midpoint coordinates = ((x1 + x2)/2, (y1 + y2)/2)

= ((2 + (-4))/2, (-8 + 12)/2)

= (-1, 2)

Step 2: Find the coordinates that are 3/4 of the way from the midpoint to point B.

Difference in x-coordinates = -4 - (-1) = -3

Difference in y-coordinates = 12 - 2 = 10

New coordinates = (midpoint x-coordinate + (3/4) * difference in x-coordinates, midpoint y-coordinate + (3/4) * difference in y-coordinates)

= (-1 + (3/4) * -3, 2 + (3/4) * 10)

= (-1 - (9/4), 2 + (30/4))

= (-1 - (9/4), 2 + 7.5)

= (-2.25, 9.5)

Therefore, the coordinates that are 3/4 of the way to point B are (-2.25, 9.5).