Question

3. Segment MN has endpoints at M(-6, -3) and N(9,7). Point Q lies on MN such that MQ:QN = 3:2.
Which of the following are the coordinates of Q? Plz I don’t want fail my sophomore year

Answer 1

Given:

Segment MN has endpoints at M(-6, -3) and N(9,7).

Point Q lies on MN such that MQ:QN = 3:2.

To find:

The coordinates of point Q.

Solution:

Section formula: If a point divides of line segment whose end points are $(x_1,y_1)$ and $(x_2,y_2)$ in m:n, then the coordinates of that points are:

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Segment MN has endpoints at M(-6, -3) and N(9,7) and Point Q lies on MN such that MQ:QN = 3:2. By using section formula, we get

$Q=\left(\dfrac{3(9)+2(-6)}{3+2},\dfrac{3(7)+2(-3)}{3+2}\right)$

$Q=\left(\dfrac{27-12}{5},\dfrac{21-6}{5}\right)$

$Q=\left(\dfrac{15}{5},\dfrac{15}{5}\right)$

$Q=\left(3,3\right)$

Therefore, the coordinates of point Q are (3,3).