Given A (4, -3) and B (-12, 13), find the point on segment AB that is three-fourths of the way from A to B.
A)( -6, 0 )
B)( -8, 9 )
C)( 0, 1 )
D)( 1, 0 )
E)( 9, -8 )

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, where A is (x1, y1) and B is (x2, y2). The formula for the x-coordinate of P is [(mx2 + nx1) / (m + n)], and for the y-coordinate of P is [(my2 + ny1) / (m + n)]. Here, the ratio is 3:1 (since the point is three-fourths of the way from A to B), A is (4, -3), and B is (-12, 13). Plugging these values into the formula gives us the coordinates of the point as (-8, 9).

Given a (4, -3) and B (-12, 13), Find the Point