Question

Points P,Q, and R are collinear such that PQ:QR = 1:2 - Point P is located at (0,1) and R is located at (9,5) Find:

A) The x and y coordinates of Q
B) The x and y coordinates of the midpoint M​

Answer 1

The x-coordinate of point Q is 3 and the y-coordinate of point Q is 7/3. The x-coordinate of the midpoint M is 4.5 and the y-coordinate of the midpoint M is 3.

Step-by-step explanation:

In order to find the x and y coordinates of point Q, we can use the given ratio of PQ:QR = 1:2 to determine the position of point Q relative to point P.

First, we find the difference in the x-coordinate between P and R, which is 9 - 0 = 9. We can divide this difference by the sum of the ratio values (1 + 2) to find the value of one part of the ratio. This gives us 9 / (1 + 2) = 3. So, the x-coordinate of point Q is 0 + 3 = 3.

Using the same approach, we find the difference in the y-coordinate between P and R, which is 5 - 1 = 4. Dividing this difference by the sum of the ratio values (1 + 2) gives us 4 / (1 + 2) = 4/3. So, the y-coordinate of point Q is 1 + 4/3 = 7/3.

Thus, the x-coordinate of point Q is 3 and the y-coordinate of point Q is 7/3.

To find the x and y coordinates of the midpoint M, we can take the average of the x and y coordinates of points P and R.

The x-coordinate of the midpoint is (0 + 9) / 2 = 4.5 and the y-coordinate of the midpoint is (1 + 5) / 2 = 3.