Question

this question has two parts. be sure to answer both parts of the question. rectangle pqrs is graphed on the coordinate - plane. both the x - and y - axes on the graph are scaled from negative ten to ten, in increments of one. the rectangle is labeled pqrs. part a rectangle pqrs is rotated ninety degrees counterclockwise about the origin to create rectangle p prime q prime r prime s prime (not shown). what are the coordinates of point r prime? a (-7,6) b (7,6) c (-6,7) d (6,7) part b rectangle pqrs is reflected across the y - axis and then translated down two units to create rectangle p double prime q double prime r double prime s double prime (not shown). what are the coordinates of q double prime?

Explanation:

Answer:

PART A

Let's assume the original coordinates of the vertices of rectangle \(PQRS\) are known. When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(-y,x)\). Without knowing the original coordinates of point \(R\), we can't give a numerical answer. But if the original coordinates of \(R\) are \((a,b)\), then \(R'\) (after \(90^{\circ}\) counter - clockwise rotation about the origin) will have coordinates \((-b,a)\)

PART B

1. First, reflection across the \(y\) - axis:

• The rule for reflecting a point \((x,y)\) across the \(y\) - axis is \((x,y)\to(-x,y)\).

1. Then, translation down 2 units:

• The rule for translating a point \((x,y)\) down 2 units is \((x,y)\to(x,y - 2)\).
• Let the original coordinates of \(Q\) be \((m,n)\). After reflection across the \(y\) - axis, the coordinates become \((-m,n)\). After translation down 2 units, the coordinates of \(Q''\) are \((-m,n - 2)\). Without knowing the original coordinates of \(Q\), we can't give a numerical answer.

Since we don't have the original coordinates of the points from the graph, we can only provide the transformation rules. If we assume we can read the original coordinates of point \(R=(x_1,y_1)\) from the graph: