Question

Quadrilateral IJKL has the following vertices. What type of quadrilateral is it? Choose the most specific answer.

Answer 1

Answer: Square.

Step-by-step explanation

Based on the coordinates given, we would have the following triangle:

A quadrilateral is a four-sided figure.

• The triangle has three sides, thus, the "isosceles triangle" option would not be the correct one.

As the other options have four sides, we have to know the measure of each side using the following formula:

`s=√(x^2+y^2)`

where x represents the distance in the horizontal axis and y represents the distance in the vertical asymptote.

The side that goes from (–5, 3) to (1, –5) would have the following values:

`x=\lvert{1-(-5)}\rvert=1+5=6`
`y=\lvert{-5-3}\rvert=8`

Now, replacing in the formula:

`s=√(6^2+8^2)=√(100)=10`

Following the same procedure from the side that goes from (1, –5) to (3, 9) we can find that, in this case, x = 8 and y = 6:

`s=√(8^2+6^2)=√(100)=10`

Using the same procedure from the side that goes from (9, 1) to (3, 9) we can find that, in this case, x = 6 and y = 8, as in the first case. Therefore, s = 10.

Finally, in the side from (3, 9) to (–5, 3), x = 8 and y = 6, same as in the second case, then s = 10.

As all the sides have equal length, then this quadrilateral is a square.