Question

one vertex of a triangle is located at (0, 5) on a coordinate grid. after a transformation, the vertex is located at (5, 0). which transformations could have taken place? choose two correct answers

Explanation:

Step1: Recall rotation rules

For a rotation of $R_{0,\theta}$ about the origin $(0,0)$ of a point $(x,y)$ to $(x',y')$:

• If $\theta=- 90^{\circ}$ (clock - wise $90^{\circ}$ rotation), the rule is $(x,y)\to(y, - x)$. So for the point $(0,5)$, we have $(0,5)\to(5,0)$.
• If $\theta = 270^{\circ}$ (counter - clockwise $270^{\circ}$ rotation), which is equivalent to a clock - wise $90^{\circ}$ rotation. The rule is also $(x,y)\to(y,-x)$. For the point $(0,5)$, we get $(0,5)\to(5,0)$.
• If $\theta = 180^{\circ}$, the rule is $(x,y)\to(-x,-y)$. For $(0,5)$, we have $(0,5)\to(0, - 5)$.
• If $\theta=-180^{\circ}$, which is the same as $180^{\circ}$ rotation, the rule is $(x,y)\to(-x,-y)$. For $(0,5)$, we get $(0,5)\to(0,-5)$.
• If $\theta = 90^{\circ}$ (counter - clockwise $90^{\circ}$ rotation), the rule is $(x,y)\to(-y,x)$. For $(0,5)$, we have $(0,5)\to(-5,0)$.

Answer:

A. $R_{0,-90^{\circ}}$
B. $R_{0,270^{\circ}}$