Given A (7, -3) and B (-9, 9), find the point on segment AB that is three-fourths of the way from A to B.
A)( 3, 0 )
B)( -6, 3 )
C)( -5, 6 )
D)( 6, -5 )
E)( 0, 3 )

Question

Quizplus · Accepted Answer

To find the point that is three-fourths of the way from A to B, we 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 $P(x, y) = \left(\frac{3(-9) + 1(7)}{3 + 1}, \frac{3(9) + 1(-3)}{3 + 1}\right) = \left(\frac{-27 + 7}{4}, \frac{27 - 3}{4}\right) = \left(\frac{-20}{4}, \frac{24}{4}\right) = (-5, 6)$.

Given a (7, -3) and B (-9, 9), Find the Point