Question

Look at triangle ABC.

Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 1, 2, and C at ordered pair 4, 2.

What is the length of side AB of the triangle?

Square root of 6
3
Square root of 18
6

Answer 1

length of side AB of the triangle is
`AB = √(18)` . Correct option C. Square root of 18

Explanation:

Here we have , Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 1, 2, and C at ordered pair 4, 2. We need to find What is the length of side AB of the triangle . Let's find out:

We know that distance between any two points
`P(x_1,y_1),Q(x_2,y_2)` is :

⇒
`Distance = √((x_2-x_1)^2+(y_2-y_1)^2)`

Here two points are :
`A(4,5), B(1,2)` , so length of AB is given by

⇒
`Distance = √((x_2-x_1)^2+(y_2-y_1)^2)`

⇒
`AB = √((1-4)^2+(2-5)^2)`

⇒
`AB = √((-3)^2+(-3)^2)`

⇒
`AB = √(9+9)`

⇒
`AB = √(18)`

Therefore , length of side AB of the triangle is
`AB = √(18)` . Correct option C. Square root of 18