To find the perimeter of the triangle formed by the points Q(1, 6), P(1, 2), and R(-4, 2), we need to calculate the lengths of the three sides of the triangle.
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Find the distance between points Q and P:
The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- For Q(1, 6) and P(1, 2): \[ d_{QP} = \sqrt{(1 - 1)^2 + (2 - 6)^2} = \sqrt{0 + (-4)^2} = \sqrt{16} = 4 \]
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Find the distance between points P and R:
- For P(1, 2) and R(-4, 2): \[ d_{PR} = \sqrt{(-4 - 1)^2 + (2 - 2)^2} = \sqrt{(-5)^2 + 0} = \sqrt{25} = 5 \]
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Find the distance between points Q and R:
- For Q(1, 6) and R(-4, 2): \[ d_{QR} = \sqrt{(-4 - 1)^2 + (2 - 6)^2} = \sqrt{(-5)^2 + (-4)^2} = \sqrt{25 + 16} = \sqrt{41} \]
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Calculate \(\sqrt{41}\):
- Approximately, \(\sqrt{41} \approx 6.4\) (using a calculator or estimation).
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Calculate the perimeter of the triangle: \[ \text{Perimeter} = d_{QP} + d_{PR} + d_{QR} = 4 + 5 + 6.4 = 15.4 \]
Thus, the perimeter of the triangle is approximately 15.4 units.
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