This is an isosceles triangle. The definition of an isosceles triangle is a triangle with at least two congruent sides and angles. If 2 angles on a triangle are congruent (in this case 45 and 45 are two congruent angles) then triangle is isosceles. Therefore the two sides of triangle will be congruent. We know that the triangle is a right triangle because it has a hypotenuse. If a triangle has a hypotenuse then it's a right triangle. We can apply the Pythagorean theorem: a^2 + b^2 = c^2
A and B are the legs and C is the hypotenuse.
We can plug C in the equation:
a^2 + b^2 = 128
What do we know about the legs of the isosceles triangle? They are congruent so a and b have to be equal. From here it's simply guess and check. Will 8 work?
8^2 + 8^2 = 128
64 + 64 = 128
128=128
Yes the value 8 works so the length of two legs of the triangle is 8.
You can take any 2 points from the table and calculate the slope, as follows:
-2-(-4) 2
m = slope = ---------- = ------ = -1/5
-5 - 5 -10
The slope-intercept form is y = mx + b. You already know m (which is -1/5), and have several points from which to choose to obtain x and y. Let's use the given point (-2, -1).
Then -1 = (-1/5)(-2) + b, or -1 = 2/5 + b. Solve for b.
-5 = 2 + 5b, so 5b = -7, and b = -7/5.
The desired equation is y = (-1/5)x - 7/5.
