Question

Prove that the following four points will form a rectangle when connected in orderby showing the diagonals are congruent. Show all work.AIO. -3). B(-4.0). C(2. 8). D(6. 5)

Answer 1

For the four points to form a rectangle, the length of the diagonals will be equal.

This means that we have to find the distance between the point BD and AC. If

BD = AC, then the four points would form a rectangle.

`\begin{gathered} Dis\tan ce\text{ betw}ee\text{n points B and D, that is BD} \\ \text{Distance betw}ee\text{n two points = }\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ BD=\text{ }\sqrt[]{(6-(-4)^2+(5-0)^2} \\ BD=\sqrt[]{10^2+5^2} \\ BD=\sqrt[]{125} \\ BD=\text{ 5}\sqrt[]{5} \end{gathered}`

Now let's find AC

`\begin{gathered} AC=\text{ }\sqrt[]{(2-0)^2+(8-(-3)^2} \\ AC=\sqrt[]{2^2+11^2} \\ AC=\sqrt[]{4+121} \\ AC=\sqrt[]{125} \\ AC=5\sqrt[]{5} \end{gathered}`

So, since BD = AC, the four points A, B, C and D would form a rectangle.