Question

1. rotation 180° about the origin

Explanation:

Step1: Find coordinates of original points

First, we determine the coordinates of points \( V \), \( G \), and \( E \) from the grid.

• Let's assume each grid square has a side length of 1 unit.
• For point \( V \): Looking at the grid, it is at \( (-4, -2) \) (4 units left of the origin on the x - axis and 2 units down on the y - axis).
• For point \( G \): It is at \( (0, -3) \) (on the y - axis, 3 units down from the origin).
• For point \( E \): It is at \( (2, -1) \) (2 units right of the origin on the x - axis and 1 unit down on the y - axis).

Step2: Apply 180° rotation rule

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

• For point \( V(-4, -2) \):

Applying the rule, \( x=-4\), so \( -x = 4 \); \( y = - 2\), so \( -y=2 \). So the image of \( V \), let's call it \( V' \), is \( (4,2) \).

• For point \( G(0, -3) \):

Applying the rule, \( x = 0\), so \( -x=0 \); \( y=-3\), so \( -y = 3 \). So the image of \( G \), let's call it \( G' \), is \( (0,3) \).

• For point \( E(2, -1) \):

Applying the rule, \( x = 2\), so \( -x=-2 \); \( y=-1\), so \( -y = 1 \). So the image of \( E \), let's call it \( E' \), is \( (-2,1) \).

Step3: Plot the new points

To complete the rotation, we plot the points \( V'(4,2) \), \( G'(0,3) \), and \( E'(-2,1) \) on the grid and connect them to form the rotated triangle.

Answer:

The coordinates of the rotated points are \( V'(4,2) \), \( G'(0,3) \), and \( E'(-2,1) \). The rotated triangle is formed by connecting these points. (If a graphical answer is expected, the triangle with vertices at \( (4,2) \), \( (0,3) \), and \( (-2,1) \) is the result of rotating the original triangle \( 180^{\circ} \) about the origin.)