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.
A = (3, -3), B = (7, -6) and C = (3, -6).
The area of the triangle BCD,
BCD is a right angled triangle.
BC = 4 and CD = 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. A = (3, -3), B = (7, -6) and C = (3, -6). The area of the triangle BCD, BCD is a right angled triangle. BC = 4 and CD = 3. Area of triangle = 12×3×4 = 6

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