Question

1. graph the image if the polygon is reflected across the y - axis. algebraic rule: ____________ 7. what type of transformation is shown? a. reflection across the line y = x. b. reflection across the x - axis. c. rotation of 90°. d. reflection across the line y=-x.

Explanation:

Step1: Recall reflection rules

For a reflection over the y - axis, the algebraic rule is $(x,y)\to(-x,y)$.

Step2: Analyze the transformation in question 7

When we reflect a point $(x,y)$ across the line $y = x$, the rule is $(x,y)\to(y,x)$. When we reflect across the x - axis, the rule is $(x,y)\to(x, - y)$. When we rotate 90° counter - clockwise about the origin, the rule is $(x,y)\to(-y,x)$ and when we reflect across the line $y=-x$, the rule is $(x,y)\to(-y,-x)$. By observing the transformation in question 7, we can see that the x and y coordinates of each point are swapped, which is the rule for reflection across the line $y = x$.

Answer:

For the first part (reflection over y - axis): $(x,y)\to(-x,y)$
For question 7: A. Reflection across the line $y = x$