SOLUTION: A triangle has vertices at (0,0), (3,3), and (-4,4). Classify the triangle by angles. What is the area of the triangle? What is the length of the longest side of the triangle?

Algebra.Com
Question 1022845: A triangle has vertices at (0,0), (3,3), and (-4,4). Classify the triangle by angles. What is the area of the triangle? What is the length of the longest side of the triangle? What is the perimeter of the triangle?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A triangle has vertices at (0,0), (3,3), and (-4,4). Classify the triangle by angles. What is the area of the triangle?
What is the length of the longest side of the triangle? What is the perimeter of the triangle?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

It is right-angled triangle.

One leg lies in the (+45°) straight line y = x and has the length .

The other leg lies in the (+135°) straight line y = -x and has the length .

This right-angled triangle has the legs ratio , hence, it is 3:4:5 right-angled triangle. 

It implies that the hypotenuse has the length .

The area is  = 3*4 = 12 square units.

The perimeter is  =  units.


RELATED QUESTIONS

A rectangle has vertices at (0,0), (0,-4), (-3,-4), and (-3,0) What is the perimeter of... (answered by solver91311)
A Rectangle has vertices at 0,0 0,-4 -3,-4 and -3,0 what is... (answered by Alan3354)
What is the area of an equilateral triangle if a point inside the triangle is at a... (answered by Fombitz,ikleyn,greenestamps)
What is the area of the triangle with vertices (1, 4), (3, 1) and (11, 1)? (answered by Edwin McCravy)
Find the area of the triangle with vertices of A(0, 0), B(3, 4), and C(4,... (answered by Alan3354)
In a Cartesian coordinates, the vertices of a triangle are defined by the following... (answered by josgarithmetic)
What’s the area of a triangle whose vertices are (-4,-3),(8,7) and (8,-3) (answered by josgarithmetic)
What is the area of a triangle whose vertices are A(2,-4), B(1,6) and... (answered by greenestamps)
A right triangle has sides of length 3 in., 4 in., and 5 in. The two shortest sides of... (answered by John10)