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.
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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: \[ \Delta y = B_y - A_y = 5 - 1 = 4 \]
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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 \( X_y \): \[ X_y = 1 + 0.92 = 1.92 \]
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Final coordinates of point \( X \): \[ X = (3.15, 1.92) \]
Thus, the coordinates of point \( X \) are \( (3.15, 1.92) \).