Question

The coordinates of the endpoints of BC are B(3,2) and C(8,17). Point D is on BC and divides it such that BD:CD is 3:2. What are the coordinates of D?

A) (4,7).
B) (5,9).
C) (6,11).
D) (7,13).

Answer 1

To find the coordinates of point D, we use the formula for dividing a line segment internally. Plugging in the values, we find that the coordinates of D are approximately (5,9).

Step-by-step explanation:

To find the coordinates of point D, we need to use the concept of dividing a line segment internally. Let's consider the line segment BC, where B is (3,2) and C is (8,17). We want to divide the line segment in the ratio 3:2. The coordinates of D can be found using the formula:

D = ((x2 * m) + (x1 * n)) / (m + n), ((y2 * m) + (y1 * n)) / (m + n)

Plugging in the values, we get: D = ((8 * 3) + (3 * 2)) / (3 + 2), ((17 * 3) + (2 * 2)) / (3 + 2)

Simplifying, D ≈ (5,9)