Question

b) rotate △abc 180° around the origin.

Explanation:

Step1: Identify original coordinates

First, we find the coordinates of points \( A \), \( B \), and \( C \) from the graph. Let's assume the grid has integer coordinates. From the graph, we can see:

• \( A \): Let's say \( A = (1, 0) \) (since it's 1 unit right on the x - axis and 0 on the y - axis)
• \( B \): \( B=(2, 3) \) (2 units right on x - axis, 3 units up on y - axis)
• \( C=(3, 0) \) (3 units right on x - axis, 0 on y - axis)

Step2: Apply 180° rotation rule

The rule for rotating a point \((x,y)\) 180° around the origin is \((x,y)\to(-x,-y)\).

For point \( A=(1,0) \):

Applying the rule, the new coordinates \( A' \) are \((- 1,0)\) (since \( x = 1\to - 1\), \( y = 0\to0\))

For point \( B=(2,3) \):

Applying the rule, the new coordinates \( B' \) are \((-2,-3)\) (since \( x = 2\to - 2\), \( y = 3\to - 3\))

For point \( C=(3,0) \):

Applying the rule, the new coordinates \( C' \) are \((-3,0)\) (since \( x = 3\to - 3\), \( y = 0\to0\))

Step3: Plot the new points

To graph the rotated triangle \( \triangle A'B'C' \), we plot the points \( A'(-1,0) \), \( B'(-2,-3) \), and \( C'(-3,0) \) and then connect them.

Answer:

The coordinates of the rotated triangle \( \triangle A'B'C' \) are \( A'(-1,0) \), \( B'(-2,-3) \), and \( C'(-3,0) \). To graph it, plot these points and connect them.