Question

A quadrilateral ABCD is drawn on a coordinate plane. Find the length of the side AB.A. 85 units B. 45 units C. 117 units D. 13 units

Answer 1

The length of the side AB of the quadrilateral is: √45 Units

How to find the distance between two coordinates?

The formula that is used to find the distance between two coordinates is:

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

To find the length of AB, we need to find the coordinates for A and B.

A(-2, 6) and B(4, 3)

Thus:

AB = √[(3 - 6)² + (4 - (-2))²]

AB = √(9 + 36)

AB = √45 Units

Answer 2

We are given a quadrilateral, and we are asked to find the length of one of its sides. To do that, let's remember the formula for the length of a line segment in a coordinated plane:

`L=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}`

Where:

`\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}`

Are the extreme points of the line segment. Therefore, we need to find the coordinates of points A and B. These are:

`\begin{gathered} A=(-2,6) \\ B=(4,3) \end{gathered}`

Now we replace these values in the formula:

`L=\sqrt[]{(3-6)^2+(4-(-2))^2}`

Solving the operations:

`L=\sqrt[]{(-3)^2+(6)^2}`
`L=\sqrt[]{9+36}=\sqrt[]{45}=6.7`

Therefore, the length is 6.7