Question

Find the distance between points K(−1, −3) and L(0, 0). Round to the nearest tenth.

Answer 1

d = √10

Explanation:

`K(-1, -3) , L(0, 0).\\\\d=√(((x_2-x_1)^2+ (y_2-y_1)^2) ) \\\\x_1 =-1\\\\y_1 =-3\\\\x_2 =0\\\\y_2 =0 \\\\d = √((0-(-1))^2+(0-(-3))^2)\\\\ d = √((0+1)^2+(0+3)^2)\\\\ d = √((1)^2 + (3)^2)\\\\ d = √(1 + 9)\\\\ d = √(10) \\`

Answer 2

`\huge\boxedKL`

Explanation:

METHOD 1:

The formula of a distance between two points (x₁; y₁) and (x₂; y₂):

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have K(-1; -3) and L(0; 0). Substitute:

`|KL|=√((0-(-3))^2+(0-(-1))^2)=√(3^2+1^2)=√(9+1)=√(10)}`

METHOD 2:

Look at the picture.

We have the right triangle with the legs 3 and 1.

Use the Pythagorean theorem:

`leg^2+leg^2=hypotenuse^2`

substitute:

`3^2+1^2=|KL|^2\\\\|KL|^2=9+1\\\\|KL|^2=10\to|KL|=√(10)`