Question

Find the coordinates of the triangle X 'Y'Z after each rotation

Answer 1

1.

A rotation of 90° clockwise about the origin will make the figure swap its x and y coordinates. Also, the figure will go from the 1st quadrant to the 4th quadrant, so its y-coordinates will be negative.

So we have:

`\begin{gathered} X(1,4)\to X^(\prime)(4,-1) \\ Y(3,1)\to Y^(\prime)(1,-3) \\ Z(1,1)\to Z^(\prime)(1,-1) \end{gathered}`

2.

A rotation of 180° about point Z will make the y-coordinate of point X decrease by 6 units (double the length of XZ) and the x-coordinate of point Y will decrease by 4 units (double the length of YZ). Point Z will be in the same location. So we have:

`\begin{gathered} X(1,4)\to X^(\prime)(1,-2) \\ Y(3,1)\to Y^(\prime)(-1,1) \\ Z(1,1)\to Z^(\prime)(1,1) \end{gathered}`

3.

A rotation of 90° ccw about point Y will make the segment YZ point downwards, so the x-coordinate of Z increases by 2 and its y-coordinate decrease by 2.

The segment ZX will point to the left, so the x-coordinate of X will be the x-coordinate of Z' minus 3, and its y-coordinate will be the same as the y-coordinate of Z'.

Y' is in the same location of Y:

`\begin{gathered} Z(1,1)\to Z^(\prime)(3,-1) \\ X(1,4)\to X^(\prime)(0,-1) \\ Y(3,1)\to Y^(\prime)(3,1) \end{gathered}`