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((mx_2+nx_1)/(m+n),(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((3(9)+2(-6))/(3+2),(3(7)+2(-3))/(3+2)\right)`

`Q=\left((27-12)/(5),(21-6)/(5)\right)`

`Q=\left((15)/(5),(15)/(5)\right)`

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

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