Question

math 8 term 1 homework #3

1. which transformation would take shape a to shape b?

a. a reflection over the y - axis
b. a reflection over the x - axis
c. a clockwise rotation of 90° about the origin
d. a clockwise rotation of 270° about the origin

1. which transformation would take shape a to shape b?

a. a reflection over the x - axis
b. a clockwise rotation of 90° about the origin
c. a reflection over the y - axis
d. a clockwise rotation of 270° about the origin

1. figure y is the result of a transformation on figure x. which transformation would accomplish this?

a. a translation 4 units up
b. a rotation 180° clockwise about the origin
c. a reflection over the y - axis
d. a reflection over the x - axis

1. figure x is the result of a transformation on figure w. which transformation would accomplish this?

a. a translation 1 unit up
b. a reflection over the x - axis
c. a reflection over the y - axis
d. a translation 1 unit down

Explanation:

Step1: Recall transformation rules

Reflection over y - axis changes (x,y) to (-x,y), over x - axis changes (x,y) to (x, - y), 90 - degree clockwise rotation about origin changes (x,y) to (y, - x) and 270 - degree clockwise rotation about origin changes (x,y) to (-y,x).

Step2: Analyze first problem

For the first problem, comparing the orientation and position of Shape A and Shape B, we see that a reflection over the y - axis would map Shape A to Shape B. The x - coordinates of corresponding points change sign while y - coordinates remain the same. So the answer for the first problem is A.

Step3: Analyze second problem

For the second problem, comparing Shape A and Shape B, a reflection over the y - axis would take Shape A to Shape B as the left - right orientation changes while the up - down orientation remains the same. So the answer for the second problem is C.

Step4: Analyze third problem

For the third problem, comparing Figure X and Figure Y, a 180 - degree clockwise rotation about the origin would map Figure X to Figure Y. When we rotate a point (x,y) 180 degrees clockwise about the origin, it becomes (-x,-y). So the answer for the third problem is B.

Step5: Analyze fourth problem

For the fourth problem, comparing Figure W and Figure X, a translation 1 unit down would map Figure W to Figure X as all the points of Figure W move 1 unit down to form Figure X. So the answer for the fourth problem is D.

Answer:

1. A. A reflection over the y - axis
2. C. A reflection over the y - axis
3. B. A rotation 180° clockwise about the origin
4. D. A translation 1 unit down