Question

3 stephen draws figure abcd in the coordinate plane. he rotates figure abcd 270° clockwise around vertex b to form image abcd. draw the image abcd in the coordinate plane. what are the coordinates of the vertices of figure abcd? show your work.
a (-2,2) b (-4,1) c (-5,0) d (-1,2)
solution
4 petra plots △abc in the coordinate plane. its vertices are at (-1, -3), (-4, -5), and (-7, -2). she then reflects the triangle across the y - axis to form its image, △abc. which coordinates represent a vertex of the image? select all the correct answers.
a (-1,3) b (1, -3) c (7, -2) d (-4,5) e (4, -5) f (-7,2)
5 samir draws △pqr in the coordinate plane as shown. then he rotates △pqr 90° counterclockwise around the origin to form △pqr. samir incorrectly says the coordinates of q are (5, -4). what is the correct answer? how might samir have gotten his answer? explain your reasoning.

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ across the $y -$axis, the rule is $(x,y)\to(-x,y)$.

Step2: Apply rule to vertices of $\triangle ABC$

For vertex $(-1,-3)$ of $\triangle ABC$, after reflection across the $y -$axis, the new vertex is $(1,-3)$.
For vertex $(-4,-5)$ of $\triangle ABC$, after reflection across the $y -$axis, the new vertex is $(4,-5)$.
For vertex $(-7,-2)$ of $\triangle ABC$, after reflection across the $y -$axis, the new vertex is $(7,-2)$.

for question 5:

Step1: Recall rotation rule

The rule for rotating a point $(x,y)$ 90° counter - clockwise around the origin is $(x,y)\to(-y,x)$.

Step2: Assume coordinates of $Q$

Let the coordinates of $Q$ be $(x,y)$. To find the correct coordinates of $Q'$ after 90° counter - clockwise rotation around the origin, we use the rule. If Samir got $(5,-4)$ wrong, he might have used the wrong rule. He might have thought the rule was $(x,y)\to(y, - x)$ (a wrong rotation or transformation rule).
Let's assume the correct coordinates of $Q$ are $(4,5)$. Using the 90° counter - clockwise rotation rule $(x,y)\to(-y,x)$, for the point $Q(4,5)$, the coordinates of $Q'$ are $(-5,4)$.

Answer:

B. $(1, - 3)$
C. $(7,-2)$
E. $(4,-5)$