Question

point d is shown in the coordinate - plane. plot the image point for each single transformation of point d. then write the coordinates. a. image a: reflection across the x - axis. b. image b: translation 7 units to the right. c. image c: rotation 90° counterclockwise around the origin. ∠h and its image ∠h are shown in the coordinate plane. what single rotation maps ∠h onto ∠h? a 90° clockwise rotation around the origin b 180° clockwise rotation around the origin c 180° counterclockwise rotation around the origin d 270° clockwise rotation around the origin kori chose a as the correct answer. how might she have gotten that answer?

Explanation:

Step1: Recall transformation rules

For a point $(x,y)$ reflected across the $x - axis$, the new point is $(x,-y)$. For a translation 7 units to the right, if the original point is $(x,y)$ the new point is $(x + 7,y)$. For a 90 - degree counter - clockwise rotation around the origin of a point $(x,y)$, the new point is $(-y,x)$.

Step2: Analyze rotation of triangle

To determine the rotation of $\triangle H$ to $\triangle H'$, we can use the fact that for a 180 - degree rotation (clockwise or counter - clockwise) around the origin, a point $(x,y)$ becomes $(-x,-y)$. By observing the orientation and position of $\triangle H$ and $\triangle H'$ in the coordinate plane, we can see that a 180 - degree rotation (either clockwise or counter - clockwise) maps $\triangle H$ onto $\triangle H'$.

Step3: Analyze incorrect answer

If Kari chose A (90 - degree clockwise rotation around the origin), she might have misidentified the orientation of the vertices of the triangle. A 90 - degree clockwise rotation of a point $(x,y)$ around the origin gives $(y,-x)$. She may have not correctly applied the rotation rule or mis - observed the relative positions of the vertices of the two triangles.

Answer:

For the transformation of point D:
a. If the coordinates of point D are $(x,y)$, the coordinates of the image after reflection across the $x - axis$ are $(x,-y)$.
b. If the coordinates of point D are $(x,y)$, the coordinates of the image after translation 7 units to the right are $(x + 7,y)$.
c. If the coordinates of point D are $(x,y)$, the coordinates of the image after 90 - degree counter - clockwise rotation around the origin are $(-y,x)$.
For the rotation of $\triangle H$ onto $\triangle H'$:
The correct answer is B. 180° clockwise rotation around the origin and C. 180° counterclockwise rotation around the origin.
Kari might have misapplied the 90 - degree clockwise rotation rule or mis - observed the triangle's vertices when she chose A as the correct answer.