Question 1079900: State how each transformation affects the area
A triangle had vertices A(2,3), B(5,2), C(5,4). The transformation is (x,y) to (x,2y)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! A(2,3), B(5,2), C(5,4) are the three given points
Double each y coordinate to get these corresponding points: A'(2,6), B'(5,4), C'(5,8)
Note: Points B' and C share the same location
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Plot the set of points on the same grid. We have these two triangles shown below
Image generated using GeoGebra (free graphing software).
The base of each triangle is actually the vertical component. If you want, rotate the image 90 degrees to have the triangles flat on one side.
The base of triangle ABC is segment BC, which is 2 units. The height is perpendicular to the base and goes from segment BC to point A. The height of triangle ABC is 3 units.
Area of triangle ABC = (1/2)*base*height
Area of triangle ABC = (1/2)*2*3
Area of triangle ABC = 0.5*2*3
Area of triangle ABC = 1*3
Area of triangle ABC = 3 square units
Triangle A'B'C' has the base B'C' which is 4 units (notice how it's double that of BC). The height is the same as the previous triangle. The height is 3 units.
Area of triangle A'B'C' = (1/2)*base*height
Area of triangle A'B'C' = (1/2)*4*3
Area of triangle A'B'C' = 0.5*4*3
Area of triangle A'B'C' = 2*3
Area of triangle A'B'C' = 6 square units
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Old area = 3 square units
New area = 6 square units
The area has been doubled.
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