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?

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) (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 . Draw this so you see it.

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

The length of the hypotenuse is:

Can we find a without using the hypotenuse?
Area formula gives ;
.

That one possible point is therefore, (4, 6).
Answer by MathTherapy(10552) (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!!

RELATED QUESTIONS
Find a and b that a>0,b>0 and the point (a,b),(1,b) and (a,6) are vertices of a triangle... (answered by math-vortex)
Question: What is the area, in square units, of the square with the four vertices at A(0, (answered by josgarithmetic)
The side of a right triangle are 8,15 and 17 units. If each side is doubled, how many... (answered by ankor@dixie-net.com)
Writing to Learn Equidistant Point from Vertices of a Right Triangle Prove that the... (answered by stanbon,ikleyn)
Two vertices of a triangle are (2, 4) and (-2, 3) and the area is 2 square units, the... (answered by josgarithmetic)
A right triangle has 6-inch, 8-inch, and 10-inch sides. A square can be inscribed in this (answered by greenestamps)
A isosceles right triangle PQR is drawn on a coordinate grid. The vertices are... (answered by Alan3354)
Three unit squares and two line segments connecting two pairs of vertices are shown. What (answered by CPhill,ikleyn)
Two vertices of a triangle are (2,4) and (-2,3) and the area is 2 square units, the locus (answered by josgarithmetic)