Home
Class 12
MATHS
Two adjacent vertices of a square are (1...

Two adjacent vertices of a square are (1, 2) and `(-2,6)` Find the other vertices.

Text Solution

Verified by Experts


Given two adjacent vertices are A (1,2) and B(-2,6). Then,
AB = 5
Also, the slope of AB is
`m_(AB) = (6-2)/(-2-1) = -(4)/(3)`
` "Slope of AD" = (3)/(4) = "tan " theta`
The coordinates of D and D' are
`(1+-5 "cos" theta, 2+-5"sin"theta) -= (1+-5(4)/(5), 2 +- 5(3)/(5))`
or D(5,5) and D'(-3-1)
Similarly, the coordinates of C and C' are
`(-2+-5 "cos" theta, 6+-5"sin"theta) -= (-2+-5(4)/(5), 6 +- 5(3)/(5))`
or C(2,9) and C'(-6,3)
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXAMPLE|12 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.1|23 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

If the two vertices of a square are (3,4)and (1,-1,) then find the coordinate of other vertices.

The coordinates of two opposite vertices of a rectangle are (1,3) and (5,1) . If other two vertices are on the line y=2x-lambda then the value of lambda will be -

The coordinates of two point opposite vertices oc a square are (3,4) and (1,-1), find the coordinates of the other two vertices.

A rectangle has two opposite vertices at the points (1, 2) and (5,5). If the other vertices lie on the line x=3 , find the other vertices of the rectangle.

(2,1) and (0,0) are the two adjcent vertices of a square. Then then perimeter of the square is

Two vertices of a triangle are (5,-1) and (-2,3) If the orthocentre of the triangle is the origin, find the coordinates of the third point.

The centroid of a tringle is (6,9) and of two its vertices are (15,0) and (0,10). Find the coordinates of the third vertex.

The vertices of a triangle are (2,-2) , (4,2) and (-1,3), Find the equation of the madian through (-1,3).

The co-ordinates of the vertices of a quadrilateral are (3,-2)(6,2)(4,3) and (-1,0) resp.Find the area of the quadrilateral.

If (0,-1) and (0,3) are two opposite vertices of a square, then the other two vertices are-