Question

1. answer the following questions and use the graph provided:

a) write the ordered pairs for abc on the blanks below.
b) write the rule for rotating a figure around the origin, 180° cw
c) write the ordered pairs for the image. then graph the image.
rule: ____ → ____
a ____ → a ____
b ____ → b ____
c ____ → c ____

Explanation:

Part a)

Step 1: Determine coordinates of A

From the graph, A is at (0, 4) (assuming the vertical line is y - axis and horizontal is x - axis, counting grid squares).

Step 2: Determine coordinates of B

B is at (2, 1) (moving 2 units right on x - axis and 1 unit up on y - axis from origin).

Step 3: Determine coordinates of C

C is at (-2, 2) (moving 2 units left on x - axis and 2 units up on y - axis from origin).

The rule for rotating a point \((x,y)\) 180° clockwise (or counter - clockwise, since 180° rotation is the same in both directions) around the origin is to change the signs of both the x - coordinate and the y - coordinate. So the rule is \((x,y)\to(-x,-y)\).

Step 1: Find \(A'\)

For point A(0, 4), using the rule \((x,y)\to(-x,-y)\), substitute \(x = 0\) and \(y = 4\). We get \(A'=( - 0,-4)=(0, - 4)\).

Step 2: Find \(B'\)

For point B(2, 1), using the rule \((x,y)\to(-x,-y)\), substitute \(x = 2\) and \(y = 1\). We get \(B'=(-2,-1)\).

Step 3: Find \(C'\)

For point C(-2, 2), using the rule \((x,y)\to(-x,-y)\), substitute \(x=-2\) and \(y = 2\). We get \(C'=(2,-2)\).

Answer:

A: (0, 4), B: (2, 1), C: (-2, 2)

Part b)