Question

1. rotation 180° about the origin

Explanation:

Step1: Find coordinates of R, S, T

First, we determine the coordinates of the original points. Let's assume each grid square has a side length of 1 unit.

• Point \( R \): Looking at the grid, if we consider the origin \((0,0)\), moving left (negative x) and up (positive y). Let's say \( R \) is at \((-7, 3)\) (we count the grid squares: from the y - axis, moving 7 units left (x=-7) and 3 units up (y = 3)).
• Point \( S \): Let's find its coordinates. From the origin, moving left 5 units (x=-5) and up 4 units (y = 4), so \( S=(-5,4) \).
• Point \( T \): From the origin, moving left 2 units (x=-2) and up 1 unit (y = 1), so \( T=(-2,1) \).

Step2: Apply 180° rotation rule

The rule for a \( 180^{\circ} \) rotation about the origin is \((x,y)\to(-x,-y)\).

• For point \( R(-7,3) \):

Applying the rule, \( x=-7\to -(-7) = 7 \), \( y = 3\to - 3=-3 \). So \( R'=(7,-3) \).

• For point \( S(-5,4) \):

Applying the rule, \( x=-5\to -(-5)=5 \), \( y = 4\to - 4=-4 \). So \( S'=(5,-4) \).

• For point \( T(-2,1) \):

Applying the rule, \( x=-2\to -(-2) = 2 \), \( y=1\to - 1=-1 \). So \( T'=(2,-1) \).

Step3: Plot the rotated points

Now, we plot the points \( R'(7,-3) \), \( S'(5,-4) \), and \( T'(2,-1) \) on the coordinate plane. Then we connect these points to get the image of \( \triangle RST \) after a \( 180^{\circ} \) rotation about the origin.

Answer:

The coordinates of the rotated points are \( R'(7, - 3) \), \( S'(5, - 4) \), and \( T'(2, - 1) \). To graph the rotated triangle, plot these points and connect them.