Question

N the diagram, and are horizontal lines and is a vertical line segment. If FB : FC = 4 : 3, what are the coordinates of point D?

Answer 1

Given the diagram, where AB and EF are horizontal lines and CB is a vertical line segment. Given that FB : FC = 4 : 3, From the diagram, the coordinate of A is (-10, -8) and the coordinate of C is (-3. -1). We can also see that the coordinate of B is (-3, -8) (since CB is a vertical line means that B is the same x-value as C and AB is a horizontal line means that B is the same y-value as A) Recall that the coordinate of a point dividing a line segment in the ratio m:n is given by (x1 + m/(m+n) (x2 - x1), y1 + m/(m+n) (y2 - y1)) Thus, since FB : FC = 4 : 3, this means that point F divides the line segment BC in the ratio 4 : 3. Thus, the coordinate of F is given by (-3 + 4/(4+3) (-3 - (-3)), -8 + 4/(4+3) (-1 - (-8))) = (-3 + 4/7 (0), -8 + 4/7 (7)) = (-3, -4). Also, given that FB : FC = 4 : 3, this means that point D divides the line segment AC in the ratio 4 : 3. Thus, the coordinate of D is given by (-10 + 4/(4+3) (-3 - (-10)), -8 + 4/(4+3) (-1 - (-8))) = (-10 + 4/7 (7), -8 + 4/7 (7)) = (-6, -4). Therefore, the coordinates of point D is (-6, -4).