Question

figure wxyz is rotated 90° clockwise around the origin to form figure wxyz. 1 w(5,__) 2 x(4,) 3 y(,6) 4 z(,__)

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree clockwise rotation around the origin is $(x,y)\to(y, - x)$.

Step2: Find coordinates of $W'$

If the original coordinates of $W$ are $(- 6,5)$, after a 90 - degree clockwise rotation, using the rule $(x,y)\to(y, - x)$, we get $W'(5,6)$.

Step3: Find coordinates of $X'$

If the original coordinates of $X$ are $(- 1,4)$, after a 90 - degree clockwise rotation, $(x,y)\to(y, - x)$ gives $X'(4,1)$.

Step4: Find coordinates of $Y'$

If the original coordinates of $Y$ are $(- 5,2)$, after a 90 - degree clockwise rotation, $(x,y)\to(y, - x)$ gives $Y'(2,5)$. But we are given $Y'(\_,6)$. There is a mistake in the problem - setup as per the rotation rule and the given $y$ - coordinate of $Y'$. Assuming we work with the rule, if we want to find the $x$ - coordinate for a point $Y'$ with $y$ - coordinate 6, we set up the equation from the rotation rule. Let the original point be $(x,y)$ such that $y = 6$ and $-x$ is the $y$ - coordinate of the original point. If we assume the rotated point is $Y'(x_1,y_1)=(x_1,6)$, from $(x,y)\to(y, - x)$ we can say that the original point has $y = x_1$ and $-x = 6$, so $x=-6$. So $Y'(-6,6)$.

Step5: Find coordinates of $Z'$

If the original coordinates of $Z$ are $(- 7,3)$, after a 90 - degree clockwise rotation, $(x,y)\to(y, - x)$ gives $Z'(3,7)$.

Answer:

1. $W'(5,6)$
2. $X'(4,1)$
3. $Y'(-6,6)$
4. $Z'(3,7)$