Question

transformations unit test. use the function rules to find the coordinates of △abc and predict the quadrant it will be in after the transformations. △abc, with coordinates a(-8,4), b(-5,8), and c(-3,3), is transformed by (x,y)→(x + 4,y - 6) to produce △abc. △abc is transformed by the rule (x,y)→(x + 5,y - 3). create the rule for the composition transformation and predict what quadrant the image will be in. (4 points). short answer rubric (4 points). points awarded criteria. 4 the answer is very clear. the answer is fully supported by details. there may be a few errors in grammar, usage, or mechanics. errors do not interfere with meaning. 3 the answer is mostly clear. the answer is supported by mostly relevant details. there are a few errors in grammar, usage, or mechanics. errors do not interfere with meaning. 2 the answer is somewhat clear. details are weak or not related. there are some errors in grammar, usage, and mechanics. errors interfere with meaning. 1 the answer is not clear. there are few or no supporting details. there are many errors in grammar, usage, and mechanics. errors interfere with meaning. 0 the question is not answered.

Explanation:

Step1: Find the composition transformation rule

First transformation: $(x,y)\to(x + 4,y - 6)$. Second transformation: $(x,y)\to(x + 5,y - 3)$. For the composition, we apply the first and then the second. If we start with $(x,y)$, after the first transformation we get $(x_1,y_1)=(x + 4,y - 6)$. Then applying the second transformation to $(x_1,y_1)$ gives $(x_2,y_2)=(x_1+5,y_1 - 3)=(x + 4+5,y - 6-3)=(x + 9,y - 9)$.

Step2: Find the new coordinates of points

For point $A(-8,4)$:
Substitute $x=-8$ and $y = 4$ into the composition rule $(x + 9,y - 9)$. We get $A''=(-8 + 9,4 - 9)=(1,-5)$.
For point $B(-5,8)$:
Substitute $x=-5$ and $y = 8$ into the rule. We get $B''=(-5 + 9,8 - 9)=(4,-1)$.
For point $C(-3,3)$:
Substitute $x=-3$ and $y = 3$ into the rule. We get $C''=(-3 + 9,3 - 9)=(6,-6)$.

Step3: Determine the quadrant

The points $A''(1,-5)$, $B''(4,-1)$ and $C''(6,-6)$ all have positive $x$-coordinates and negative $y$-coordinates. So the image $\triangle A''B''C''$ is in the fourth - quadrant.

Answer:

The composition transformation rule is $(x,y)\to(x + 9,y - 9)$ and the image $\triangle A''B''C''$ is in the fourth quadrant.