Question

Drag each tile to the correct box.
Triangle ABC has the following vertices.

A( -6, 1) B(6, 1) C(6, 6)

List the sides of the triangle in order from largest length to smallest length.

Coordinate plane with all four quadrants. The both axes are labeled from -6 to 6.



AB
BC
CA
> >

Answer 1

To find the lengths of the sides of triangle ABC, we can use the distance formula, which is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

### Step 1: Calculate the lengths of each side

1. **Length of side AB**:
Points A(-6, 1) and B(6, 1):
\[
AB = \sqrt{(6 - (-6))^2 + (1 - 1)^2} = \sqrt{(6 + 6)^2 + 0^2} = \sqrt{12^2} = 12
\]

2. **Length of side BC**:
Points B(6, 1) and C(6, 6):
\[
BC = \sqrt{(6 - 6)^2 + (6 - 1)^2} = \sqrt{0^2 + (6 - 1)^2} = \sqrt{0 + 5^2} = \sqrt{25} = 5
\]

3. **Length of side CA**:
Points C(6, 6) and A(-6, 1):
\[
CA = \sqrt{(6 - (-6))^2 + (6 - 1)^2} = \sqrt{(6 + 6)^2 + (6 - 1)^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13
\]

### Step 2: List the side lengths

- AB = 12
- BC = 5
- CA = 13

### Step 3: Order the sides from largest to smallest

1. CA (13)
2. AB (12)
3. BC (5)

### Final Arrangement
- CA
- AB
- BC

So, the order from largest length to smallest length is:

- CA
- AB
- BC