Answer:
Your third point should be above D at (5,-1) to form a right triangle.
Step-by-step explanation:
Easiest way is draw a vertical line at point D and a horizontal line at point C, where they intersect will be (5,-1) which will form a right triangle.
Still need convincing? Let's solve it by the fact that if we're talking about right triangles, we can use Pythagorean theorem.
By Pythagorean theorem we have:
[tex]c^2=a^2+b^2[/tex]
Where c is the hypotenuse (CD), and a and b are the shorter of the three legs of the triangle.
Therefore,
[tex]c=\sqrt{a^2+b^2}=\sqrt{(x_2-x_1)^2)+(y_2-y_1)^2} = \sqrt{9^2+(-5)^2}[/tex]
We don't need to evaluate what c is but it is [tex]\sqrt{106}[/tex], what we need to focus on is the 9^2 and (-5)^2. The first number 9^2 tells us that from C we must move 9 units to the right or (-5)^2 means 5 units up from point D which will return the same answer (5,-1). So one of the legs is 5 units long, the other is 9 units long and the hypotenuse is [tex]\sqrt{106}[/tex] units long.
