Question

The coordinates of the endpoints of overline BC are B(-11,6) and C(5,-10). Point D is on overline BC and divides it such that BD:CD is 7:1.

What are the coordinates of D?
Write your answers as integers or decimals.

Answer 1

The coordinates of point D, which divides the line segment BC in the ratio 7:1, are calculated using the section formula to be (3, -8).

Step-by-step explanation:

The coordinates of the endpoints of overline BC are B(-11,6) and C(5,-10). Point D is on overline BC and divides it in the ratio of BD:CD as 7:1. To determine the coordinates of point D, we can use the section formula in the midpoint form:

M(x, y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n)),

where M is the point dividing the line segment with endpoints (x1, y1) and (x2, y2) internally in the ratio m:n.

Applying this formula:

D(x, y) = (((7 * 5) + (1 * -11)) / (7 + 1), ((7 * -10) + (1 * 6)) / (7 + 1))

D(x, y) = ((35 - 11) / 8, (-70 + 6) / 8)

D(x, y) = (24 / 8, -64 / 8)

D(x, y) = (3, -8)

The coordinates of point D are (3, -8).

.