Question

Point T is on a segment with endpoints R(5, 10) and V(11, 4). Point T divides the segment such that RT:TV is 5:1. What are the coordinates of T?

Answer 1

We want to find a point on a segment such that the point divides the segment in the ratio 5:1

We will find that the point T is (6, 9)

The general formula for the point T that divides a segment whose endpoints are (x₁, y₁) and (x₂, y₂) such that separates the segment in the ratio j:k is given by:

$T = (\frac{j*x_1 + k*x_2}{j + k} , \frac{j*y_1 + k*y_2}{j + k})$

Here we have the endpoints (5, 10) and (11, 4), and we know that the ratio is 5:1

Then we can just use the above formula to get:

$T = (\frac{5*5 + 1*11}{5 + 1} , \frac{5*10 + 1*4}{5 + 1}) = (\frac{36}{6} , \frac{54}{6} ) = (6, 9)$

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