Math

Two vertices of a right triangle are (0,1) and (0,6). The area of the triangle is 10 square units. Which point could be the third vertex of the triangle?

  1. 👍 0
  2. 👎 0
  3. 👁 284
  1. let's consider (0,1) and (0,6) to be the base,
    the the base is 5 units.
    let the height be h
    giving us a nice isosceles triangle

    (1/2)(5)h = 10
    5h = 20
    h = 4

    so a possible third point is (4, 3.5)

    As a matter of fact, we could now take any point along the vertical line x = 4
    Since x = 4 is parallel to the y-axis, the distance between them is always 4 and the base of our triangle is always 5, giving us an area of
    (1/2)(4)(5) = 10

    A third point looks like (4, k), where k is any real number.

    1. 👍 0
    2. 👎 0
  2. Forgot to mention that we could also have placed out third point on the left side of the y-axis,
    e.g. (-4,8) would work

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. 8th Grade Pre-Algebra

    Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(3, −6), Q(0, 9), and R(−3, 0). Triangle P'Q'R' has vertices P'(1, −2), Q'(0, 3), and R'(−1, 0). Plot triangles PQR and P'Q'R' on your own

  2. math Ms. Sue

    A right triangle has an area of 13 m2. The dimensions of the triangle are increased by a scale factor of 3. What is the area of the new triangle? 39 m2 169 m2 117 m2 142 m2 I think it is A...?

  3. Pre-Algebra

    A right triangle has an area of 21 m2. The dimensions of the triangle are increased by a scale factor of 4. What is the area of the new triangle? A. 42 m2 B. 84 m2 C. 168 m2 D. 336 m2 How would I solve this?

  4. calculus

    a right triangle is formed in the first quadrant by the x- and y- axes and a line through the point (1,2). write the length of the hypotenuse as a function of x. find the vertices of the triangle such that its area is a minimum.

  1. Geometry

    R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. m

  2. Math

    Triangle ABC has vertices A (-4,-2), B (-1,3), and C (5,0). Triangle ABC is rotated 180 degrees counterclockwise about the origin to form triangle A'B'C'. a. what are the coordinates of the vertices of triangle A'B'C'? b. How

  3. Math III

    Which of the following statements are true? a. the incenter of a triangle is equidistant from all three vertices of that triangle b. The incenter of a triangle always lies inside that triangle c. the incenter of a triangle is the

  4. Geometry

    The vertices of a triangle are P(-3,8), Q(-6, -4), and R (1, 1). Name the vertices of R (smaller letters)y-0 (triangle PQR). A. P'(-3, 8), Q'(-6,-4), R'(1,1) B. P'(-3,-8), Q'(-6,4), R'(1,-1) C. P'(3,-8), Q'(6,4), R'(-1,-1) D. P'

  1. Math HELP

    #1 find the value of x if RS = 4(x-3)+6 and RT = 5(2x-6). x= 12 x= 6 x= 4*** x= 3 #2 which of the following statements are always true? Choose all that apply. If the circumcenter of a triangle lies on the triangle, then the

  2. Math 7th

    Triangle ABC is shown on the graph below. link to picture a. Triangle ABC is reflected over the y-axis. What are the coordinates of the reflected triangle? b. Describe in words what happens to the x-coordinates and the

  3. math

    Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(3, −6), Q(0, 9), and R(−3, 0). Triangle P'Q'R' has vertices P'(1, −2), Q'(0, 3), and R'(−1, 0). Plot triangles PQR and P'Q'R' on your own

  4. algebra

    The points (1,2), (5,5),(1,6) are the vertices of a shaded triangle. a. Write a system of linear inequalities represented by the shaded triangle. b. Find the area of the triangle.

You can view more similar questions or ask a new question.