Unit 5, Lesson 5
Scaling and Unscaling
Geometry
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A triangle has an area of 6 square inches and a perimeter of 12 inches. Suppose it is dilated by some scale factor, and the area and perimeter of the image are calculated. Match each graph with the relationship it represents.
Graph AA graph. X axis from 0 to 70 by 10’s. Y axis from 0 to 3 by 1’s. Line begins at the origin, moves upward and to the right through about 10 comma 1 point 2 5, 40 comma 2 point 5, and ends around 80 comma 3 point 5.
Graph BA graph. X axis from 0 to 70 by 10’s. Y axis from 0 to 7 by 1’s. Line begins at the origin and moves upward and to the right through about 10 comma point 7 5, 30 comma 2 point 5, and ends around 80 comma 6 point 5.
Graph CA graph. X axis from 0 to 7 by 1’s. Y axis from 0 to 70 by 10’s. Line begins at the origin and moves upward and to the right through about 1 comma 12, 3 comma 35, and ends around 6 point 5 comma 80.
Graph DA graph. X axis from 0 to 3 by 1’s. Y axis from 0 to 70 by 10’s. Line begins at the origin, moves upward and to the right through about point 5 comma 5, 2 point 5 comma 25, and ends around 3 point 5 comma 80.
Graph A
Graph B
Graph C
Graph D
scale factor is the \(x\)-value; perimeter is the \(y\)-value
scale factor is the \(x\)-value; area is the \(y\)-value
perimeter is the \(x\)-value; scale factor is the \(y\)-value
area is the \(x\)-value; scale factor is the \(y\)-value
Parallelogram \(AB’C’D'\) was obtained by dilating parallelogram \(ABCD\) using \(A\) as the center of dilation.
Select all expressions that give the measure of angle \(A\).
\(\arccos\left(\frac{28}{53}\right)\)
\(\arccos\left(\frac{45}{53}\right)\)
\(\arcsin\left(\frac{28}{53}\right)\)
\(\arcsin\left(\frac{45}{53}\right)\)
\(\arctan\left(\frac{28}{45}\right)\)
\(\arctan\left(\frac{45}{28}\right)\)