Question

7. Segment MN has endpoints at M(-12,-5) and N(8, 10). A third point Q is located on MN such that MQ:ON=2:3. Answer the following questions. (a) Find the coordinates of Q. Show how you arrived at your answer.​

Answer 1

To find the coordinates of Q, we can use the concept of proportional division of line segments.

Given that MQ:ON = 2:3, it means that the ratio of the length of MQ to ON is 2:3.

Let's first find the vector that represents the direction of MN, which is the vector pointing from M to N. We can find this by subtracting the coordinates of M from the coordinates of N:

(8,10) - (-12,-5) = (20, 15)

This is the vector <20,15>

Now, we can find the point Q, which is located two thirds of the way from M to N, by multiplying the vector <20,15> by 2/5 and adding the result to the coordinates of M:

Q = M + (2/5) * <20,15>

= (-12,-5) + (2/5) * <20,15>

= (-12,-5) + <8,6>

= (8,1)

So, the coordinates of Q are (8,1)