Question

The coordinates of the endpoints of

BC

are B(

–

10,

–

7) and C(0,

–

2). Point D is on

BC

and divides it such that BD:CD is 3:2.

What are the coordinates of D?

Write your answers as integers or decimals.

Answer 1

Using the section formula, the coordinates of point D that divides the line segment BC with endpoints B(–10,–7) and C(0,–2) in the ratio 3:2 are found to be (-6, -5).

Step-by-step explanation:

To find the coordinates of point D that divides line segment BC in the ratio 3:2, we can use the section formula. The coordinates of the endpoints of BC are given as B(–10,–7) and C(0,–2). Using the section formula to find the coordinates of D, which divides BC internally in the ratio of m:n (in this case, m=3 and n=2), is:

Dx = (mb_x + nc_x) / (m + n)

Dy = (mb_y + nc_y) / (m + n)

Plugging in the values:

Dx = (3*(-10) + 2*(0)) / (3 + 2)

= (-30 + 0) / 5

= -30/5

= -6

Dy = (3*(-7) + 2*(-2)) / (3 + 2)

= (-21 - 4) / 5

= -25/5

= -5

So the coordinates of point D are (-6, -5).