Question

question #4. skill:___________from unit 5, lesson 2consider triangle abc graphed here.here are some transformation rules. for each transformation, first predict what the image of triangle abc will look like. then compute the coordinates of the image and draw it.a. $(x,y) \to (x - 4, y - 1)$prediction:coordinates of image:b. $(x,y) \to (y, x)$prediction:coordinates of image:

Explanation:

Step1: Identify original coordinates

From the graph: $A=(2,3)$, $B=(4,2)$, $C=(3,5)$

Step2: Solve transformation (a): translate

Apply $(x,y)\to(x-4,y-1)$:
$A'=(2-4, 3-1)=(-2,2)$
$B'=(4-4, 2-1)=(0,1)$
$C'=(3-4, 5-1)=(-1,4)$

Step3: Predict transformation (a)

Translation: 4 left, 1 down, same shape/size.

Step4: Solve transformation (b): reflect over $y=x$

Apply $(x,y)\to(y,x)$:
$A''=(3,2)$
$B''=(2,4)$
$C''=(5,3)$

Step5: Predict transformation (b)

Reflection over line $y=x$, mirrored shape.

Answer:

Part a

Prediction:

Triangle $ABC$ will translate 4 units left and 1 unit down, maintaining its original size and shape.

Coordinates of image:

$A'=(-2, 2)$, $B'=(0, 1)$, $C'=(-1, 4)$

Part b

Prediction:

Triangle $ABC$ will be reflected over the line $y=x$, resulting in a mirrored triangle with the same size and shape.

Coordinates of image:

$A''=(3, 2)$, $B''=(2, 4)$, $C''=(5, 3)$