Question

I am an isosceles triangle. The midpoint of my non-congruent side is the point (7, −2). This side is a horizontal line with a length of 4 and my vertex opposite this side is at the point (7, −7). Oh, I almost forgot to tell you. I am upside down. Where am I? (Find the coordinates of each base vertex.) 2 answers a small and large x-value

Answer 1

So, we can picture out the problem that this is an inverted triangle. So, the base of the triangle is along y = -2. All we have to find are the x coordinates. The main formula we will use here is the distance formula for computing distance between any 2 points.

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

The solution is as follows:

D between (7,-2) and (7,-7).
d = √[(7 - 1)² + (-7 - -2)²] = 5 units
Let's solve the hypotenuse.
h = √(5² + (4/2)²) = √29
So, the distance of the hypotenuse is the distance between the top vertex (7,-7) and one bottom side vertex (x,-2) is √29.
√29 = √[(x - 7)² + (-2 - -7)²]
Solving for x,
x = 5
Since the base is 4 units in length, the other base vertex is at x = 5 - 4 = 1
Therefore, the vertex of the bases of the isosceles triangle are at (5,-2) and (1,-2).