Question

What are the coordinates of point X
if it is located 23
of the way from A
to B
?
coordinate: A(2,1) B(7,5)
(1 point)

Answer 1

To find the coordinates of point \( X \) that is located \( \frac{23}{100} \) (or 0.23) of the way from point \( A(2, 1) \) to point \( B(7, 5) \), you can use the section formula.

1. **Find the change in coordinates**:

The difference in the x-coordinates:
\[
\Delta x = B_x - A_x = 7 - 2 = 5
\]

The difference in the y-coordinates:
\[
\Delta y = B_y - A_y = 5 - 1 = 4
\]

2. **Calculate the coordinates of point \( X \)**:

Since point \( X \) is \( 0.23 \) of the way from \( A \) to \( B \), you can find the coordinates of \( X \) using the following formulas:

\[
X_x = A_x + 0.23 \cdot \Delta x = 2 + 0.23 \cdot 5
\]
\[
X_y = A_y + 0.23 \cdot \Delta y = 1 + 0.23 \cdot 4
\]

Now, calculate \( X_x \):
\[
X_x = 2 + 1.15 = 3.15
\]

And calculate \( X_y \):
\[
X_y = 1 + 0.92 = 1.92
\]

3. **Final coordinates of point \( X \)**:
\[
X = (3.15, 1.92)
\]

Thus, the coordinates of point \( X \) are \( (3.15, 1.92) \).