geometry

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.

  1. 👍 0
  2. 👎 0
  3. 👁 352
asked by katie
  1. 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

    1. 👍 0
    2. 👎 0
    posted by MathMate

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math Urgent Please Help

    Which coordinates could be the vertices of a triangle similar to triangle RST? {original triangle coordinates R(0,0); S(0,4); T(3,0)} a. (2,2), (2,6), and (6,0)*** b. (0,0), (0,6), and (10,0) c. (2,2), (2,10), and (6,2) d. (0,0),

    asked by Mame on June 3, 2016
  2. math

    Which point has the coordinates(-0.5,- 2.5 )? A.point A B.point B*** C.point C D.point D What are the coordinates of point C? A. (-1, 2) B. (- 2,2) C. ( 1.5 ,2)*** D. (- 1.5, 2) Which statement is true about the ordered pair

    asked by Street fighter on April 13, 2019
  3. 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'.

    asked by Angel on January 18, 2011
  4. 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)

    asked by Mary on June 30, 2008
  5. math,algebra II

    can someone show me examples of what is a practical application of matrices or matrix operations that can be used in a real-world situation. Simple example: Coordinate transformation. An object is located at coordinates (x,y,z) in

    asked by jas on June 5, 2007
  6. math

    There are 2 similar triangles. 1 has coordinates (2,3)(3,4)(2,7). The other has coordinate (7,6) and letter A for the right corner of the base and P for the top. A has coordinates 1)(9,8) 2)(10,9) 3)(7.5,6.5) For each case find

    asked by Anonymous on January 13, 2008
  7. Math

    Triagle abc is reflected over the y-axis what are the coordinates of the refected triangle describe in words what happens to the x coordinates and the y coordinates of the orignal triangle's vertices as a result of this reflection

    asked by Please Help on March 22, 2016
  8. math

    Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down. A)Write the coordinated of the vertices of the image after reflection. B)Write a rule for the translation. Use arrow rotation.

    asked by gwen on May 18, 2014
  9. maths

    the mid-point of the line FG is (6,10). if the coordinates of G is (8,14) find the coordinates of F. There are a number of ways to solve this but I think the simplest is to use the definiton of midpoint. We know mdpt(FG) =

    asked by Jen on September 7, 2006
  10. 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.

    asked by Ginny on April 24, 2011

More Similar Questions