Question

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 8 to 8 in increments of 1. A triangle A B C is plotted on the graph. The triangle A B C has its vertices marked with closed points at A left parenthesis 2 comma 6 right parenthesis, B left parenthesis 6 comma 4 right parenthesis, and C left parenthesis 2 comma 2 right parenthesis.

Given point A(2, 6) on the triangle, what are the new coordinates of the point after the triangle is rotated 180 degrees counterclockwise?

(1 point)
(
)

Answer 1

Question
Use the image to answer the question.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 8 to 8 in increments of 1. Three rectangles are formed by lines joining four plotted points each. Two of the rectangles are joined by rays connecting complementary vertices. The coordinates of the plotted points for the rectangle in quadrant 4 are left parenthesis 1 comma negative 3 right parenthesis, left parenthesis 1 comma negative 7 right parenthesis, left parenthesis 4 comma negative 7 right parenthesis, and left parenthesis 4 comma negative 3 right parenthesis. The coordinates for the rectangle in quadrant 2 are left parenthesis negative 2 comma 1 right parenthesis, left parenthesis negative 6 comma 1 right parenthesis, left parenthesis negative 6 comma 4 right parenthesis, and left parenthesis negative 2 comma 4 right parenthesis. The coordinates of the plotted points for the rectangle in quadrant 3 are left parenthesis negative 3 comma negative 1 right parenthesis, left parenthesis negative 7 comma negative 1 right parenthesis, left parenthesis negative 7 comma negative 4 right parenthesis, and left parenthesis negative 3 comma negative 4 right parenthesis. Four rays from each vertex of the rectangle in quadrant 3 connect to the complementary vertices of the rectangle in quadrant 2. A ray connects the point left parenthesis negative 7 comma negative 4 right parenthesis to left parenthesis negative 6 comma 1 right parenthesis. A ray connects the point left parenthesis negative 7 comma negative 1 right parenthesis to left parenthesis negative 6 comma 4 right parenthesis. A ray connects the point left parenthesis negative 3 comma negative 4 right parenthesis to left parenthesis negative 2 comma 1 right parenthesis. A ray connects the point left parenthesis negative 3 comma negative 1 right parenthesis to left parenthesis negative 2 comma 4 right parenthesis. The arrow heads are on the vertices of the rectangle in quadrant 2.
How would you describe the series of transformations that have occurred to move the rectangle in Quadrant IV to the rectangle in Quadrant II to show that the rectangles are congruent?(1 point)
Responses

rotation, then reflection
rotation, then reflection

reflection, then translation
reflection, then translation

translation, then rotation
translation, then rotation

rotation, then translation

Answer 2

answer

Answer 3

The new coordinates of point A after the triangle is rotated 180 degrees counterclockwise can be determined by reflecting the point across the x-axis and then the y-axis.

First, reflecting across the x-axis will change the y-coordinate to its negative value. So, the new y-coordinate of point A will be -6.

Next, reflecting across the y-axis will change the x-coordinate to its negative value. So, the new x-coordinate of point A will be -2.

Therefore, the new coordinates of point A after the triangle is rotated 180 degrees counterclockwise are (-2, -6).