To find the coordinates of point P’ after translating point P (7, 4) 4 units to the left and 8 units down, we can follow these steps:
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Translate 4 units to the left:
- From x = 7, moving left by 4 units gives us: \[ 7 - 4 = 3 \]
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Translate 8 units down:
- From y = 4, moving down by 8 units gives us: \[ 4 - 8 = -4 \]
So the coordinates of point P’ are (3, -4).
Next, we need to calculate the distance between points P (7, 4) and P’ (3, -4). We can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] where (x₁, y₁) = (7, 4) and (x₂, y₂) = (3, -4).
Calculating step-by-step:
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Calculate \(x_2 - x_1\): \[ 3 - 7 = -4 \]
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Calculate \(y_2 - y_1\): \[ -4 - 4 = -8 \]
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Square the differences: \[ (-4)^2 = 16 \quad \text{and} \quad (-8)^2 = 64 \]
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Sum the squared differences: \[ 16 + 64 = 80 \]
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Take the square root: \[ d = \sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5} \]
To find a numerical approximation for \( \sqrt{5} \), we can use the fact that \( \sqrt{5} \) is approximately 2.236: \[ d \approx 4 \times 2.236 \approx 8.944 \]
This is approximately 8.9, which, rounding to one decimal place, is 8.9.
Thus, the answer is: A. 8.9