# geometry

posted by .

in an equilateral triangle RST, R has coordinates (0.0)and T has coordinate of (2a,0).Find the coordinates of S in terms of a.

• geometry -

By symmetry, S must lie on the vertical line x=a.
Let the coordinates of S be (a,y).
Since the length of one side of the triangle is (2a-0)=2a, we can calculate the distance of (a,y) to (0,0) and equate to 2a accordingly.

Using Pythagoras theorem,
(2a)=sqrt(a²+y²)
Solving for y:
y²=(2a)²-a²=3a²
y=(√3)a

## Similar Questions

1. ### algebra

1).Map. On a map, the coordinates of the corners of a town are A(0.5),B(2,3.5), C(5,1.5), and D(3,1) The map is dilated so that the perimeter of the town is five times its original perimeter. Find the coordinates of C. a. (25,7.5) …
2. ### algebra

graph triangle rst with vertices r(-1,3),s(4,-2), t(2,-5) Draw the image triangle r's't' formed by rotating triangle rst 90 degree, 180 degrees, and 270 degrees about the origin. Give the coordinates of r',s', and t'.
3. ### geometry

Triangle PQR has vertices P(1,2), Q(25,2) and R(10,20). Find the coordinates of the centroid. Find the coordinates of the circumcenter. Find the coordinates of the orthocenter. Find the equation of the line.
4. ### geometry

The coordinates of the vertices of a triangle are A(1,3), B(6,10), and C(11,18). Find the perimeter of the triangle when the coordinates are multiplied by 3.
5. ### Geometry

Suppose the coordinate of P is 2, PQ = 8, and PR = 12. What are the possible coordinates of the midpoint of the given segment?
6. ### geometry

the coordinate of p are (-2,5) and the coordinates of q are (6,1). a.what is the slope of pq?
7. ### geometry

The coordinates of the vertices of triangle CDE are C(1,4), D(3,6), and E(7,4). If the triangle is reflected over the line y=3, what are the coordinates of the image of D?
8. ### Algebra hw, coordinates!! help!!

Triangle ABC has coordinates A(1, 4); B(3, –2); and C(4, 2). Find the coordinates of the image A'B'C' after a reflection over the x-axis.