SOLUTION: Two vertices of a right triangle are (0,1) and (0,6). The area of the triangle is 10 square units. Which point could be the third vertex of the triangle?

Algebra ->  Triangles -> SOLUTION: Two vertices of a right triangle are (0,1) and (0,6). The area of the triangle is 10 square units. Which point could be the third vertex of the triangle?      Log On


   

Question 825317: Two vertices of a right triangle are (0,1) and (0,6). The area of the triangle is 10 square units. Which point could be the third vertex of the triangle?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
This has four different possible solutions. Try using (0,1) and (0,6) to be the segment of one of the legs. Another point may be (a, 6), for a%3E0. Draw this so you see it.

The lengths of the two legs are:
5, and a.

The length of the hypotenuse is:
sqrt%28%286-1%29%5E2%2B%28a-0%29%5E2%29
sqrt%2825%2Ba%5E2%29

Can we find a without using the hypotenuse?
Area formula gives %281%2F2%29a%2A5=10;
a=%282%2F1%29%281%2F5%2910=4.

That one possible point is therefore, (4, 6).

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Two vertices of a right triangle are (0,1) and (0,6). The area of the triangle is 10 square units. Which point could be the third vertex of the triangle?

What are the points? There are 4!!