Question

a reflection over the y - axis

1. the table below shows the coordinates of a figure that was transformed.

which is a correct description of the transformation?
a. rotation 180° clockwise
b. reflection over the x - axis
c. translation 5 units left and 2 units down
d. translation 10 units left and 4 units down

1. if jkl is rotated 180° clockwise, which describes the location of j’?

a. (-7,6)
b. (6,7)
c. (7, - 6)
d. (7,6)

Explanation:

Step1: Analyze rotation 180° rule

When a point \((x,y)\) is rotated \(180^{\circ}\) clockwise about the origin, the transformation rule is \((x,y)\to(-x,-y)\).

Step2: Analyze reflection over x - axis rule

When a point \((x,y)\) is reflected over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\).

Step3: Analyze translation rule

For a translation \(a\) units left and \(b\) units down, the rule is \((x,y)\to(x - a,y - b)\).

Step4: Check each option for pre - image and image

For option A (rotation \(180^{\circ}\) clockwise):
If \(A(5,2)\) is rotated \(180^{\circ}\) clockwise, using \((x,y)\to(-x,-y)\), we get \(A'(- 5,-2)\).
For option B (reflection over \(x\) - axis):
If \(A(5,2)\) is reflected over \(x\) - axis, we get \((5,-2)
eq A'(-5,-2)\).
For option C (translation \(5\) units left and \(2\) units down):
If \(A(5,2)\) is translated \(5\) units left and \(2\) units down, we get \((5 - 5,2 - 2)=(0,0)
eq A'(-5,-2)\).
For option D (translation \(10\) units left and \(4\) units down):
If \(A(5,2)\) is translated \(10\) units left and \(4\) units down, we get \((5-10,2 - 4)=(-5,-2)\).
Check for \(B(6,1)\):
For translation \(10\) units left and \(4\) units down: \((6-10,1 - 4)=(-4,-3)=B'\).
Check for \(C(4,5)\):
For translation \(10\) units left and \(4\) units down: \((4-10,5 - 4)=(-6,1)=C'\).

Answer:

D