Question

The quadrilateral ABCD has vertices A(-4, -3), B(-3, 2), C(2, 4), and D(4, -3). Find the perimeter of ABCD. Round your answer to the nearest tenth.

Answer 1

Ok, so

Let me draw the quadrilateral here below:

What we have to do here, is to find the distance between each segment, and then sum all of them.

Let's start with segment AD.

Notice that there's a horizontal line, so the distance will be:

8 units.

Now, let's go with segment AB.

For this, we use the next equation:

Where (x1,y1) and (x2,y2) are our points.

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

So, the distance will be:

So, the segment AB has a measure of √26 units.

Now, let's go with segment BC.

B (-3 , 2) and C ( 2 , 4 )

We apply the same equation:

So, the lenght of segment BC measures √27 units.

Now and finally, let's go with segment CD.

C ( 2 , 4 ) and D ( 4 , -3 )

Finally, we sum all the measures of all sides.

And the perimeter will be:

8 + √26 + √27 + √53

= 25.57528

If we round to the nearest tenth:

Perimeter = 25.6