Question

Graph the quadrilateral WXYZ with vertices W(–4, –1), X(–6, 1), Y(–8, –1), and Z(–6, –3). Rotate the figure 90° counterclockwise and graph the rotation.

Answer 1

Option C

Explanation:

When you rotate a point you could rotate it in Clockwise direction because that's how the hand of a clock move, or rotate it in Counterclockwise direction that's the opposite rotation. In math, counterclockwise is defined as being a positive rotation while clockwise is defined as being a negative rotation. Rotating a whole shape means we're rotating every point in the shape.

On the coordinate plane, consider the point (x,y). To rotate this point by 90° around the origin in counterclockwise direction, you can always swap the x- and y-coordinates and then multiply the new x-coordinate by -1. In a mathematical language this is as follows:

`(x,y)\rightarrow(-y,x)`

By applying this rule to every point we have:

`W(-4, -1) \rightarrow W'(1, -4) \\ \\X(-6, 1) \rightarrow X'(-1, -6) \\ \\ Y(-8, -1) \rightarrow Y'(1, -8) \\ \\ Z(-6, -3) \rightarrow Z'(3, -6)`

The figure below shows the original shape in green while the rotated shape is the one in red. As you can see, this figure matches the option C.