To find the value of \( x \) for point D, we can first determine the equation of the line that passes through points A and C, and then we can use that equation to find the value of \( x \) when \( y = 4 \), since point D is at (x, 4).
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Identify Points A and C:
- Point A is at \( (0, 12) \)
- Point C is at \( (9, 0) \)
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Calculate the slope (m) of line AC:
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Applying this to points A and C: \[ m = \frac{0 - 12}{9 - 0} = \frac{-12}{9} = -\frac{4}{3} \] -
Use point-slope form to find the equation of the line:
The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \] Using point A (0, 12) and slope \( -\frac{4}{3} \): \[ y - 12 = -\frac{4}{3}(x - 0) \] Simplifying this equation: \[ y - 12 = -\frac{4}{3}x \] \[ y = -\frac{4}{3}x + 12 \] -
Find the value of \( x \) for point D where \( y = 4 \): We set \( y = 4 \) in the line equation: \[ 4 = -\frac{4}{3}x + 12 \] Rearranging gives: \[ -\frac{4}{3}x = 4 - 12 \] \[ -\frac{4}{3}x = -8 \] Multiplying both sides by \(-\frac{3}{4}\): \[ x = -8 \cdot -\frac{3}{4} = 6 \]
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Conclusion:
Thus, the value of \( x \) for point D is: \[ \boxed{6} \]
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