Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
On a number line, the co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.
d(R, P) + d(P, Q) = d(R, Q)
Co-ordinates of the pair of a point is given below. Hence find the distance between the pair.
3, 6
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
-9, -1
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
x + 3, x - 3
Find the distance between the following pair of points
(1, 2) and (4, 3)
Find the distance between the following pair of points
(3, −9) and (−2, 3)
Show that the following points taken in order to form the vertices of a parallelogram
A(−3, 1), B(−6, −7), C(3, −9) and D(6, −1)
If the points A(2, 0), B(– 6, 0), C(3, a – 3) lie on the x-axis then the value of a is _____
If (x + 2, 4) = (5, y – 2), then the coordinates (x, y) are _____
Find the distance with the help of the number line given below.
d(K, O)
