A few days ago
Help with geometry homework!!!?
Here is the question…
If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex. (I got this part, but its the next part that confuses me) How many of these triangles are possible?
Top 1 Answers
A few days ago
Favorite Answer
There are two possible triangles. Let`s consider the one in quadrant 1. Think of the base as the y-axis from y = 0, at the origin, to y = 4. The third vertex will be on the line y = 2 (half way between 0 and 4). let the x value of this point be P. because the triangle is equilateral, then OP ( the line fro the origin to P ) is 4. Use Pythagoras` Theorem in the right angled triangle formed by dropping a perpendicular from P on to the x-axis. Call this point A, and you get:
4^2 = 2^2 + (AP)^2, so
(AP)^2 = 16 – 4, so
AP = rt 12, so
AP = 2rt3.
So the third vertex in the first quadrant is (2rt3, 2)
The second triangle is formed by the reflection of (2rt3, 2) in the y-axis, and that is (-2rt3, 2).Hope this helps, Twiggy.
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