Question

1. rotate $overline{ab}$ 90° clockwise around the point $(-2, 1)$

bonus: find ab

1. draw all the lines of symmetry symmetry/lines of reflection on abcd below.

Explanation:

BONUS: Find \( AB \)

First, we need to determine the coordinates of points \( A \) and \( B \) from the grid. Let's assume the grid has a scale where each square is 1 unit.

Looking at the grid:

• Point \( A \) appears to be at \( (1, 3) \) (assuming the origin is at the intersection of the axes, and moving 1 unit right on the x - axis and 3 units up on the y - axis from the origin).
• Point \( B \) appears to be at \( (4, 1) \) (4 units right on the x - axis and 1 unit up on the y - axis from the origin).

To find the length of \( \overline{AB} \), we use the distance formula between two points \( (x_1,y_1) \) and \( (x_2,y_2) \), which is \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \)

Step 1: Identify the coordinates

Let \( (x_1,y_1)=(1,3) \) (coordinates of \( A \)) and \( (x_2,y_2)=(4,1) \) (coordinates of \( B \))

Step 2: Substitute into the distance formula

First, calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):
\( x_2 - x_1=4 - 1 = 3 \)
\( y_2 - y_1=1 - 3=- 2 \)

Then, find the squares of these differences:
\( (x_2 - x_1)^2=(3)^2 = 9 \)
\( (y_2 - y_1)^2=(-2)^2 = 4 \)

Next, sum these squares:
\( (x_2 - x_1)^2+(y_2 - y_1)^2=9 + 4=13 \)

Finally, take the square root:
\( AB=\sqrt{13}\approx3.61 \) (if we want a decimal approximation) or we can leave it as \( \sqrt{13} \)

Answer:

The length of \( AB \) is \( \boldsymbol{\sqrt{13}} \) (or approximately \( \boldsymbol{3.61} \))