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# The point A(3,4) is reflected over the X-axis to B.

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The point  A(3,4) is reflected over the X-axis to B. Then B  is reflected over the line y = -x to C . What is the area of triangle ABC?

Nov 7, 2020

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$$A(3,4)$$ reflected over the X-axis is $$B(-3,4)$$.
$$B(-3,4)$$ reflected over y=-x is $$(-y,-x)$$ which means that C is $$C(-4,3)$$
If we create an imaginary rectangle, the area of that is 7. Subtract the corners, and we get $$7-\frac{1}{2}-\frac{7}{2}=3$$