the base of an isoceles triangle lies on the x-axis. The coordinates of the midpoints of the equal sides pf the triangle are (2,3) and (-2,3). What are the coordinates of the vertices of the triangles? Please help.
The three vertices for this question is (4,0), (-4,0), (0,6). In order to get this you need to first start by using the distance formula and substitute the midpoints. The answer you will get is(4,0). Because it is equal the other will be (-4,0). And just take one of the points and by using the midpoint formula calculate the third point which is (0,6).
To find the coordinates of the vertices of the isosceles triangle, we need to determine the coordinates of the base vertex and the two vertices forming the equal sides.
Given that the base lies on the x-axis, we can assume that the y-coordinate of the base vertex is 0.
Let's label the coordinates of the base vertex as (x, 0).
The midpoint formula states that the coordinates (x₁, y₁) and (x₂, y₂) of a line segment's midpoint are given by:
x = (x₁ + x₂) / 2 and y = (y₁ + y₂) / 2
In our case, we have the midpoints of the equal sides: (2, 3) and (-2, 3).
Using the midpoint formula, we can set up the following equations:
x = (2 + x) / 2 => 2x = 2 + x => x = 2
x = (-2 + x) / 2 => 2x = -2 + x => x = -2
So, the x-coordinate of the base vertex is 2 when using the midpoint (2,3), and -2 when using the midpoint (-2,3).
Now that we have the x-coordinate for the base vertex, we can substitute it into (x, 0) to find the vertex coordinates.
For (2, 0), the coordinates of the base vertex are (2, 0) and the equal sides' midpoints are (2, 3) and (-2, 3).
For (-2, 0), the coordinates of the base vertex are (-2, 0), and the equal sides' midpoints are (2, 3) and (-2, 3).
Therefore, the coordinates of the vertices of the isosceles triangle are:
Vertex 1: (2, 0)
Vertex 2: (2, 3)
Vertex 3: (-2, 3)