Question

I need help right now!!!!

Choose Yes or No to tell whether each statement is correct.
Coordinate plane showing triangle A B C with coordinates A 4, 1; B negative 1, 4; and C negative 1, 1.

BC is 2 units long.
Choose...


CA is 5 units long.
Choose...


BC is shorter than BA.
Choose...


AC is 2 units longer than BC.
Choose...

Answer 1

no, yes, yes, no

Explanation:

BC is 3 units long, CA is 5 units long, BC is shorter than BA by a little over 3 units (use pythagorean theorem), and AC is longer than BC by 3 units not 2.

Answer 2

BC is not 2 units long; CA is not 5 units long; BC is shorter than BA; AC is not 2 units longer than BC.

• BC is 2 units long.

- No. The length of BC can be found using the distance formula:
`\(√((x_2 - x_1)^2 + (y_2 - y_1)^2)\).`

`\[BC = √(((-1) - (-1))^2 + (1 - 4)^2) = √(0^2 + 3^2) = 3 \text{ units}\]`

• CA is 5 units long.

- No. Similarly, using the distance formula for CA:

`\[CA = √((4 - (-1))^2 + (1 - 1)^2) = √(5^2 + 0^2) = 5 \text{ units}\]`

• BC is shorter than BA.

- Yes. Comparing the lengths using the distance formula:

`\[BA = √(((-1) - 4)^2 + (4 - 1)^2) = √((-5)^2 + 3^2) = √(25 + 9) = √(34) \text{ units}\]`

BC is 3 units, which is shorter than
`\(√(34)\)`.

• AC is 2 units longer than BC.

- No. The length of AC is 5 units, while BC is 3 units. The difference is
`\(5 - 3 = 2\)` units, so AC is not 2 units longer than BC.