A(-5,-2),B(-2,-5) andC(-12,-5) are vertices of a triangle. find the image of the triangle when It is reflected in y axis followed by a reflection in y=-x
Question
A(-5,-2),B(-2,-5) andC(-12,-5) are vertices of a triangle. find the image of the triangle when It is reflected in y axis followed by a reflection in y=-x
Solution
Step 1: Reflect the points in the y-axis
The reflection of a point (x, y) in the y-axis is (-x, y). So, we reflect the points A, B, and C in the y-axis:
A' = (5, -2) B' = (2, -5) C' = (12, -5)
Step 2: Reflect the points in the line y = -x
The reflection of a point (x, y) in the line y = -x is (y, x). So, we reflect the points A', B', and C' in the line y = -x:
A'' = (-2, 5) B'' = (-5, 2) C'' = (-5, 12)
So, the image of the triangle ABC when it is reflected in the y-axis followed by a reflection in the line y = -x is the triangle with vertices A''(-2, 5), B''(-5, 2), and C''(-5, 12).
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