Question

Anybody know the answer?

Answer 1

Method 1.

Use the formula of a distance between two points:

`A(x_A;\ y_A),\ B(x_B;\ y_B)\\\\d=√((x_B-x_A)^2+(y_B-y_A)^2)`

We have

`A(-4,\ 5)\to x_A=-4,\ y_A=5\\B(2,\ -3)\to x_B=2,\ y_B=-3`

substitute

`|AB|=√((-3-5)^2+(2-(-4))^2)=√((-8)^2+6^2)=√(64+36)=√(100)=10`

Answer: 10

Method 2

Look at the picture.

Use the Pythagorean theorem:

`x^2=6^2+8^2\\\\x^2=36+64\\\\x^2=100\to x=√(100)\\\\x=10`

Answer: 10