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  $AB = \sqrt{18}$ . Correct option C. Square root of 18

Step-by-step 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 :

⇒ $Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

⇒ $Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

⇒ $AB = \sqrt{(1-4)^2+(2-5)^2}$

⇒ $AB = \sqrt{(-3)^2+(-3)^2}$

⇒ $AB = \sqrt{9+9}$

⇒ $AB = \sqrt{18}$

Therefore , length of side AB of the triangle is  $AB = \sqrt{18}$ . Correct option C. Square root of 18