Question

1. a rectangle is plotted on the grid on the right. which image shows a 90° clockwise rotation about the origin?
2. point a(-2, -10) is reflected over the x - axis. what are the coordinates of a?

a. (-2, -10) b. (2, 10) c. (-2, 10) d. (2, -10)

1. describe the transformation done on △rts to form △vxw

a. rotation around the origin 180°
b. reflection over the x - axis
c. reflection over the y - axis
d. translation

1. △qrs is translated 4 units left and 4 units up. how do the x - coordinates of the vertices change?

a. the x - coordinates increase by 4 because 4 is a positive number.
b. the x - coordinates decrease by 4 because “left” indicates a negative change.
c. the x - coordinates decrease by 4 because 4 is a positive number.
d. the x - coordinates increase by 4 because “left” indicates a positive change.

Explanation:

7.

Step1: Recall reflection rule over x - axis

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

Step2: Apply the rule to point A

For point $A(-2,-10)$, with $x=-2$ and $y = - 10$, after reflection over the $x$-axis, we get $(-2,-(-10))=(-2,10)$.

Step1: Analyze transformation types

For a rotation of $180^{\circ}$ around the origin, the rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$. A reflection over the $x$-axis is $(x,y)\to(x, - y)$ and over the $y$-axis is $(x,y)\to(-x,y)$. A translation moves the figure without rotating or reflecting.

Step2: Observe the triangles

When we compare $\triangle RTS$ and $\triangle VXW$, we can see that the orientation of the triangles is reversed and the signs of both $x$ and $y$ - coordinates of corresponding points are changed. This is characteristic of a $180^{\circ}$ rotation around the origin.

Step1: Recall translation rule for x - coordinates

In a translation, moving left or right affects the $x$-coordinate and moving up or down affects the $y$-coordinate. Moving left means subtracting from the $x$-coordinate and moving right means adding to the $x$-coordinate.

Step2: Determine the change in x - coordinates

Since $\triangle QRS$ is translated 4 units left, for any vertex $(x,y)$ of the triangle, the new $x$-coordinate will be $x-4$. So the $x$-coordinates of the vertices decrease by 4 because moving left indicates a negative change in the $x$-direction.

Answer:

C. $(-2,10)$

8.