Back to Exercise: Represent and describe transformations

Exercises: Represent and Describe Transformations

Work through each section in order. Show your reasoning where indicated.

Grade 9·21 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-co-a-2

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Warm-Up: Review What You Know

These problems review skills from earlier courses.

A function $f$ takes inputs and produces exactly one output for each input. Which statement best describes how a geometric transformation is like a function?

A transformation moves a figure, but leaves the rest of the plane unchanged.

A transformation maps every point in the plane to exactly one image point, just as a function maps each input to one output.

A transformation only works on points that are part of a named figure.

A transformation can map one point to two different image points at the same time.

Point $P$ has coordinates $(3, -1)$ . Which of the following correctly applies the rule $T(x, y) = (x + 2, y - 4)$ to find the image of $P$ ?

$(5, -5)$

$(1, 3)$

$(3, -5)$

$(5, -1)$

Which of the following is NOT one of the four basic geometric transformations?

Translation

Reflection

Projection

Dilation

Fluency Practice

Apply the given coordinate rule to find image coordinates. Show your computation.

$Coordinate plane showing triangle ABC with a dashed arrow indicating the translation direction from vertex A.$

Triangle $ABC$ has vertices $A(1, 2)$ , $B(4, 2)$ , and $C(2, 5)$ . A translation maps every point by the rule $T(x, y) = (x + 3, y - 1)$ .

What are the coordinates of $A'$ , the image of $A$ under $T$ ? Enter the $x$ -coordinate.

Using the same triangle $ABC$ with $A(1, 2)$ , $B(4, 2)$ , $C(2, 5)$ and translation $T(x, y) = (x + 3, y - 1)$ .

What is the $y$ -coordinate of $C'$ , the image of $C(2, 5)$ under $T$ ?

$Coordinate plane showing triangle PQR and its reflection over the y-axis. The y-axis is the line of reflection.$

Triangle $PQR$ has vertices $P(2, 3)$ , $Q(5, 3)$ , $R(4, 6)$ . It is reflected over the $y$ -axis using the rule $M(x, y) = (-x, y)$ .

What is the $x$ -coordinate of $P'$ , the image of $P(2, 3)$ after reflection over the $y$ -axis?

A $90^\circ$ counterclockwise rotation about the origin follows the rule $R(x, y) = (-y, x)$ . Which point is the image of $(3, 5)$ under this rotation?

$(5, 3)$

$(-5, 3)$

$(3, -5)$

$(-3, -5)$

A dilation centered at the origin with scale factor $3$ maps triangle $DEF$ to $D'E'F'$ . Which statement is true about the distances and angles?

All distances are preserved; all angles are preserved. The dilation is a rigid motion.

All distances are tripled; all angles are preserved. The dilation is not a rigid motion.

All distances and all angles are tripled.

All angles are preserved; therefore the dilation is a rigid motion.

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