A triangle has vertices (1, 4), (1, 1), and (−3, 1). The triangle is dilated by a scale factor of 2, then translated 5 units up, and then rotated 90° counterclockwise about the origin. What are the vertices of the image of the triangle

Answer 1

dilation takes (x,y)->(2x,2y)
translation takes (x,y)->(x,y+5)
rotation takes (x,y)->(-y,x)

So, combining, we get

(x,y) -> (2x,2y) -> (2x,2y+5) -> (-2y-5,2x)

So, just apply that to each coordinate. For example,

(4,3)-> (-11,8)

Answer 2

1. The new vertices would be (-13,2) and (-7,2) and (-7,-6)
2. x = -1 and y = 2
3. William scored 26 and Porter scored 28

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