Question

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

a) D(2,-2)
b) D(-4,4)
c) D(-1,1)
d) D(3,-3)

Answer 1

To find the coordinates of point D, we can use the section formula to calculate the weighted average of the coordinates of the endpoints. By substituting the given coordinates into the formula, we can determine that the coordinates of point D are D(11/4, -8).

Step-by-step explanation:

To find the coordinates of point D, we can use the concept of section formula. The section formula states that the coordinates of a point dividing a line segment in a given ratio can be found by taking the weighted average of the coordinates of the endpoints. In this case, since the ratio BD:CD is 7:1, we can calculate the coordinates of D as:

D(x, y) = (7 * x-coordinate of C + 1 * x-coordinate of B) / (7 + 1), (7 * y-coordinate of C + 1 * y-coordinate of B) / (7 + 1)

Substituting the given coordinates into the formula, we get:

D(x, y) = (7 * 5 + 1 * -11) / 8, (7 * -10 + 1 * 6) / 8 = (33 - 11) / 8, (-70 + 6) / 8 = 22/8, -64/8 = 11/4, -8

Therefore, the coordinates of point D are D(11/4, -8).