Question

5) The points A(-9,2) B(-2,2) and C (-2,7) are connected to form ABCa) reflect abc across the y axis and label the new coordinates of each new point b) Translate abc into the fourth quadrant so that vertex A” has coordinates (2.-6)

Answer 1

`\begin{gathered} a)\text{ }A^(\prime)\text{ = (9, 2), }B^(\prime)\text{ = (2, 2), }C^(\prime)\text{ = (2, 7)} \\ b)\text{ }B^(\prime)\text{ = (9, -6), }C^(\prime)\text{ = (9, -1)} \end{gathered}`

Step-by-step explanation:

The points: A(-9,2) B(-2,2) and C (-2,7)

a) We need to reflect across the y axis:

`\begin{gathered} (x,\text{ y) }\rightarrow\text{ (}-x,\text{ y)} \\ So\text{ we will negate each of the x coordinate in the 3 vertices} \end{gathered}`
`\begin{gathered} A\colon\text{ (-9, 2) }\rightarrow\text{ (-(-9), 2)} \\ A^(\prime)\text{ = (9, 2)} \\ B\colon\text{ (-2, 2)}\rightarrow(-(-2),\text{ 2)} \\ B^(\prime)\text{ = (2, 2)} \\ C\colon\text{ (-2,7)}\rightarrow(\text{(-(-2),7)} \\ C^(\prime)\text{ = (2, 7)} \end{gathered}`

On the graph:

b) We need to get the coordinate of A'' to be (2, -6)

`\begin{gathered} \text{From A }\rightarrow\text{ A''} \\ \text{From (-9, 2) }\rightarrow\text{ (2, -6), we ne}ed\text{ to find the translation that occurred} \\ (-9\text{ +11},\text{ 2 - 8) = (2, -6)} \\ We\text{ say a translation of 11 units to the right (we are adding 11 to x coordinate)} \\ \text{And also a translation of 8 units down (we are subtracting 8 units from the y coordinate)} \end{gathered}`
`\begin{gathered} \text{Applying the rule (x, y) }\rightarrow(x+11,\text{ y -8) to other vertice:} \\ B\colon\text{ from }\mleft(-2,2\mright)\text{ }\rightarrow(-2+_{}11,\text{ 2-8)} \\ B^(\prime)\text{ = (9, -6)} \\ \\ C\colon from\text{ }\mleft(-2,7\mright)\text{ }\rightarrow\text{ (-2+11, 7-8)} \\ C^(\prime)\text{ = (9, -1)} \end{gathered}`