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
Write your answer as integer or decimals

Answer 1

To find the coordinates of point D, which divides the line segment BC in the ratio BD:CD = 7:1, we can use the section formula.

Let the coordinates of point B be \( B(-11, 6) \) and the coordinates of point C be \( C(5, -10) \). The formula for finding the coordinates of a point that divides a line segment in the ratio \( m:n \) is given by:

\[
D\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)
\]

In this case, \( m = 7 \) and \( n = 1 \), \( (x_1, y_1) = (-11, 6) \), and \( (x_2, y_2) = (5, -10) \).

Now we substitute these values into the formula:

1. Calculate the x-coordinate of D:

\[
x_D = \frac{7 \cdot 5 + 1 \cdot (-11)}{7 + 1}
= \frac{35 - 11}{8}
= \frac{24}{8}
= 3
\]

2. Calculate the y-coordinate of D:

\[
y_D = \frac{7 \cdot (-10) + 1 \cdot 6}{7 + 1}
= \frac{-70 + 6}{8}
= \frac{-64}{8}
= -8
\]

Therefore, the coordinates of point D are:

\[
D(3, -8)
\]