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

length of side AB of the triangle is   . 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 is :

⇒

Here two points are : , so length of AB is given by

⇒

⇒

⇒

⇒

⇒

Therefore , length of side AB of the triangle is   . Correct option C. Square root of 18

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)