Unit 2, Lesson 10
Dilations on a Square Grid
Accelerated 7
Practice
Problem 1
Triangle \(ABC\) is dilated using \(D\) as the center of dilation with scale factor 2.
The image is triangle \(A’B’C’\). Clare says the 2 triangles are congruent, because their angle measures are the same. Do you agree? Explain your reasoning.
Triangle A B C, it‘s image after dilation triangle A prime B prime C prime and point D. Point D is on the right, smaller triangle A B C is in the middle and larger image triangle A prime, B prime and C prime is on the right.
Problem 2
Sketch the image of quadrilateral \(PQRS\) under the following dilations:
- The dilation centered at \(R\) with scale factor 2.
- The dilation centered at \(O\) with scale factor \(\frac{1}{2}\).
- The dilation centered at \(S\) with scale factor \(\frac{1}{2}\).
Quadrilateral P Q R S and point O on a square grid. Let the lower left corner be (0 comma 0). Then the coordinates of P Q R S are P(7 comma 6), Q(5 comma 4), R(9 comma 3), S(11 comma 5). The coordinates of point O are O(5 comma 1).
Problem 3
The diagram shows 3 lines with some marked angle measures.
Find the missing angle measures.
A line slanting up and to the right. Two lines intersect this line, both slanting up and to the right, but do not intersect. At the first intersection, the top right angle is labeled 71 degrees. The rest are labeled a, b, and c. At the second intersection, the top right angle is labeled 57 degrees. The rest are labeled d, e, and f.
Problem 4
Describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q.