Advertisements
Advertisements
Question
Show that the following points taken in order to form the vertices of a parallelogram
A(−7, −3), B(5, 10), C(15, 8) and D(3, −5)
Advertisements
Solution
AB = `sqrt((5 + 7)^2 + (10 + 3)^2`
= `sqrt((12)^2 + (13)^2`
= `sqrt(144 + 169)`
= `sqrt(313)`
BC = `sqrt((15 - 5)^2 + (8 - 10)^2`
= `sqrt(10^2 + (-2)^2`
= `sqrt(100 + 4)`
= `sqrt(104)`
CD = `sqrt((3 - 15)^2 + (-5 - 8)^2`
= `sqrt((-12)^2 + (- 13)^2`
= `sqrt(144 + 169)`
= `sqrt(313)`
AD = `sqrt((3 + 7)^2 + (-5 + 3)^2`
= `sqrt((10)^2 + (-2)^2`
= `sqrt(100 + 4)`
= `sqrt(104)`
AB = CD = `sqrt(313)` and BC = AD = `sqrt(104)` ...(Opposite sides are equal)
∴ ABCD is a parallelogram.
APPEARS IN
RELATED QUESTIONS
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = 1, y = 7
Sketch proper figure and write the answer of the following question.
If A- B - C and l(AC) = 11, l(BC) = 6.5, then l(AB) = ?
Sketch proper figure and write the answer of the following question.
If X-Y-Z and l(XZ) = `3sqrt7`, l(XY) = `sqrt7`, then l(YZ) = ?
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
- 4, 5
Find the distance between the following pair of points
(3, −9) and (−2, 3)
Determine whether the given set of points are collinear or not
(a, −2), (a, 3), (a, 0)
Verify that the following points taken in order to form the vertices of a rhombus
A(3, −2), B(7, 6), C(−1, 2) and D(−5, −6)
The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, What are the coordinates of A?
The point whose ordinate is 4 and which lies on the y-axis is _______________
Find the distance with the help of the number line given below.
d(B, E)
