Question

Determine the coordinates of point T  that divides  AB¯¯¯¯¯¯¯¯ into two segments in the ratio 1:3. Write your responses as decimal values (if necessary) to the hundredths place.(1 point)T is located at (,).

Answer 1

To determine the coordinates of point T that divides segment AB in the ratio 1:3, we first need the coordinates of points A and B. Let's say the coordinates are:

- A (x1, y1)
- B (x2, y2)

The formula for finding the coordinates of a point that divides the segment AB in the ratio m:n is given by:

\[
T \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)
\]

For the ratio 1:3, we have \(m = 1\) and \(n = 3\). Plugging these values into the formula gives:

\[
T \left( \frac{1 \cdot x_2 + 3 \cdot x_1}{1 + 3}, \frac{1 \cdot y_2 + 3 \cdot y_1}{1 + 3} \right)
\]

This simplifies to:

\[
T \left( \frac{x_2 + 3x_1}{4}, \frac{y_2 + 3y_1}{4} \right)
\]

Now, please provide the specific coordinates of points A and B so that we can calculate the exact coordinates of point T.