Home
Class 12
MATHS
If the midpoints of the sides of a trian...

If the midpoints of the sides of a triangle are `(2,1),(-1,-3),a n d(4,5),` then find the coordinates of its vertices.

Text Solution

Verified by Experts

The correct Answer is:
`(7,9),(-3,-7),(1,1)`
Let the vertices of triangle be `(x_1,y_1),(x_2,y_2)`, and `(x_3,y_3)`. Then,
`(x_1+x_2)/(2)=2,(x_2+x_3)/(2),=-1,(x_3+x_1)/(2)=4`
Solving,we get `x_1=7,x_2=-3`, and `x_3=1`.
Similarly, `y_1=9,y_2=-7` and ` y_3=1`.
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.4|8 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.5|5 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.2|8 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

If the midpoints of the sides of a triangle are (2,1),(-1,-3), and (4,5), then find the coordinates of its vertices.

If the coordinates of the mid-points of the sides of a triangle be (3,-2),(-3,1) and (4,-3), then find the coordinates of its vertices.

The coordinates of the middle points of the sides of a triangle are (1, 1), (2, 3) and (4, 1) , find the coordinates of its vertices.

if the coordinates of the mid points of the sides of a triangle are (1,2),(0,-1) and (2,-1). Find the coordinates of its vertices ':

If the coordinates of the mid-points of the sides of a triangle are (1, 1) , (2, -3) and (3, 4). Find the coordinates of the centroid.

If the coordinates of the mid-points of the sides of a triangle are (1,1),(2,-3) and (3,4), find the vertices of the triangle.

The mid-points of the sides of a triangle are (1, 2), (0,-1) and (2, -1). Find the coordinates of the vertices of a triangle with the help of two unknowns.

The mid-points of the sides of a triangle are given by (3, 2, -4), (9, 8, -15) and (5, 4, 6). Find the coordinates of its vertices.