Given A (2, -1) and B (-6, 7), find the point on segment AB that is three-fourths of the way from A to B.
A)( 1, 0 )
B)( 5, -4 )
C)( 0, 1 )
D)( -4, 5 )
E)( -2, 0 )

Question

Quizplus · Accepted Answer

To find the point that is three-fourths of the way from A to B, we can use the formula for finding a point P(x, y) that divides the segment AB in the ratio m:n, which is $P(x, y) = \left(\frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n}\right)$. Here, $x_1, y_1$ are the coordinates of A, and $x_2, y_2$ are the coordinates of B. Since the point is three-fourths of the way from A to B, the ratio m:n is 3:1. Plugging in the values, we get $P(x, y) = \left(\frac{3(-6) + 1(2)}{3 + 1}, \frac{3(7) + 1(-1)}{3 + 1}\right) = \left(\frac{-18 + 2}{4}, \frac{21 - 1}{4}\right) = \left(\frac{-16}{4}, \frac{20}{4}\right) = (-4, 5)$.

Given a (2, -1) and B (-6, 7), Find the Point