QuestionAugust 27, 2025

Delta PQR is located at P(-3,-3),Q(0,0) and R(3,-3) Which statement correctly classifies Delta PQR Delta PQR is a scalene triangle. Delta PQR is an isosceles triangle. Delta PQR is an equilateral triangle. Delta PQR is a obtuse triangle.

Delta PQR is located at P(-3,-3),Q(0,0) and R(3,-3) Which statement correctly classifies Delta PQR Delta PQR is a scalene triangle. Delta PQR is an isosceles triangle. Delta PQR is an equilateral triangle. Delta PQR is a obtuse triangle.
Delta PQR is located at P(-3,-3),Q(0,0) and R(3,-3) Which statement correctly classifies Delta PQR
Delta PQR is a scalene triangle.
Delta PQR is an isosceles triangle.
Delta PQR is an equilateral triangle.
Delta PQR is a obtuse triangle.

Solution
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Answer

\Delta PQR is an isosceles triangle. Explanation 1. Calculate the distance between points Use **distance formula** d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. - PQ = \sqrt{(0 - (-3))^2 + (0 - (-3))^2} = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2} - QR = \sqrt{(3 - 0)^2 + (-3 - 0)^2} = \sqrt{3^2 + (-3)^2} = \sqrt{18} = 3\sqrt{2} - RP = \sqrt{(3 - (-3))^2 + (-3 - (-3))^2} = \sqrt{6^2 + 0^2} = \sqrt{36} = 6 2. Classify the triangle based on side lengths Since PQ = QR and RP is different, \Delta PQR has two equal sides.

Explanation

1. Calculate the distance between points<br /> Use **distance formula** $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.<br />- $PQ = \sqrt{(0 - (-3))^2 + (0 - (-3))^2} = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$<br />- $QR = \sqrt{(3 - 0)^2 + (-3 - 0)^2} = \sqrt{3^2 + (-3)^2} = \sqrt{18} = 3\sqrt{2}$<br />- $RP = \sqrt{(3 - (-3))^2 + (-3 - (-3))^2} = \sqrt{6^2 + 0^2} = \sqrt{36} = 6$<br /><br />2. Classify the triangle based on side lengths<br /> Since $PQ = QR$ and $RP$ is different, $\Delta PQR$ has two equal sides.
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