P(3, 3), Q(7, 6) and R(3, 6) are the coordinates of a triangle. A, B and C are the reflection points of P, Q and R respectively about Y = 0. The area of the triangle formed by the points B, C and D(3, -9) is ___.

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Solution

Reflection about Y = 0, X-Coordinate remain same and Y-Coordinate sign changes.
Here, A = (3, -3), B = (7, -6) and C = (3, -6).
BCD is a right-angled triangle
So, BC = 7 - 3 = 4 units and CD = (-9 - (-6)) = -3
Area of triangle = $\frac{1}{2} \times 3 \times 4$
= 6

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P(3, 3), Q(7, 6) and R(3, 6) are the coordinates of a triangle. A, B and C are the reflection points of P, Q and R respectively about Y = 0. The area of the triangle formed by the points B, C and D(3, -9) is ___.

Reflection about Y = 0, X-Coordinate remain same and Y-Coordinate sign changes. Here, A = (3, -3), B = (7, -6) and C = (3, -6). BCD is a right-angled triangle So, BC = 7 - 3 = 4 units and CD = (-9 - (-6)) = -3 Area of triangle = 12×3×4 = 6

Reflection about Y = 0, X-Coordinate remain same and Y-Coordinate sign changes.
Here, A = (3, -3), B = (7, -6) and C = (3, -6).
BCD is a right-angled triangle
So, BC = 7 - 3 = 4 units and CD = (-9 - (-6)) = -3
Area of triangle = $\frac{1}{2} \times 3 \times 4$
= 6