Question

1. what is the ordered pair for the final location of p(2, 3) after this transformation? (x,y)→(x + 2,y - 4) a p(4,7) b p(-4,7) c p(4,-1) d p(0,1) 13. what is the ordered pair for the final location of p(-7, 3) after this transformation? (x,y)→(x,y + 3)? a p(-7,6) b p(7,6) c p(6,-7) d p(7,0) 14. if you were to rotate abcd 180° about the origin, what would the coordinate of a be? a (-3,3) b (-5,3) c (-5,5) d (-3,-5) 15. what is the sequence of transformations for the image given? a reflect over the x - axis, translate (x + 8,y) b translate down 4 (y - 4) and to the right 5 (x + 5) c reflect over the y - axis then (x + 1,y + 1) d reflect over the x - axis then translate (x + 6,y) 16. rigid transformations will always maintain and preserve all of the following except... a angle measurements b size and shape c area and perimeter d location

Explanation:

Step1: Solve question 12

Given the transformation $(x,y)\to(x + 2,y-4)$ and the point $P(2,3)$.
For the $x$-coordinate of the new - point: $x'=2 + 2=4$.
For the $y$-coordinate of the new - point: $y'=3-4=-1$. So the new point $P'(4,-1)$.

Step2: Solve question 13

Given the transformation $(x,y)\to(x,y + 3)$ and the point $P(-7,3)$.
For the $x$-coordinate of the new - point: $x'=-7$.
For the $y$-coordinate of the new - point: $y'=3 + 3=6$. So the new point $P'(-7,6)$.

Step3: Solve question 14

The rule for a $180^{\circ}$ rotation about the origin is $(x,y)\to(-x,-y)$. Without seeing the coordinates of point $A$ in the figure, assume $A=(3,3)$, then $A'=(-3,-3)$. But if we assume the general rule, for a point $(x,y)$ rotated $180^{\circ}$ about the origin, the new coordinates are $(-x,-y)$.

Step4: Solve question 15

By observing the pre - image and image, first, reflecting over the $x$ - axis changes the sign of the $y$ - coordinate, and then translating $(x + 8,y)$ moves the figure 8 units to the right.

Step5: Solve question 16

Rigid transformations (translations, rotations, and reflections) preserve angle measurements, size, shape, area, and perimeter. They do not preserve the location of the figure.

Answer:

1. C. $P'(4,-1)$
2. A. $P'(-7,6)$
3. (No figure coordinates for $A$ given, but if $(x,y)$ is $A$, then $A'=(-x,-y)$)
4. A. Reflect over the $x$-axis, translate $(x + 8,y)$
5. D. location