Question

What is the area of the rectangle whose coordinates are at A(-1, 4), B(3, 2), Clo,-4) and D(-4,-2)? (Round to the nearest whole number.)

Answer 1

The area of the rectangle is 36 square units

Here, we want to find the area of the rectangle

To do this, we need the distance between two points

As we know, the area of a rectangle is the product of its sides with the length of parallel sides being equal

Now, let us find the distance between two points then multiply

Let us find the distance between AB and AC; after which we can multiply

The distance between two points formula is given below;

`\begin{gathered} D\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ (x_1,y_1)\text{ = (-1,4)} \\ (x_2,y_2)\text{ = (3,2)} \\ \text{This is for AB as follows;} \\ D\text{ = }\sqrt[]{(2-4)^2+(3+1)^2}\text{ = }\sqrt[]{20} \\ \text{for ; AC, we have;} \\ D\text{ = }\sqrt[]{(-1-0)^2+(4+4)^2}\text{ =}\sqrt[]{65} \end{gathered}`

So, we have the area as the product of this two;

`\sqrt[]{20\text{ }}\text{ }*\text{ }\sqrt[]{65}\text{ = }\sqrt[]{1,300\text{ }}\text{ = 36 sq.units}`