Advertisements
Advertisements
प्रश्न
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)
Advertisements
उत्तर
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((-6 + 3)^2 + (-7 - 1)^2`
= `sqrt((- 3)^2 + (- 8)^2`
= `sqrt(9 + 64)`
= `sqrt(73)`
BC = `sqrt((3 + 6)^2 + (-9 + 7)^2`
= `sqrt(9^2 + (-2)^2`
= `sqrt(81 + 4)`
= `sqrt(85)`
CD = `sqrt((6 - 3)^2 + (-1 + 9)^2`
= `sqrt((3)^2 + (8)^2`
= `sqrt(9 + 64)`
= `sqrt(73)`
AD = `sqrt((6 + 3)^2 + (-1 - 1)^2`
= `sqrt((9)^2 + (-2)^2`
= `sqrt(81 + 4)`
= `sqrt(85)`
AB = CD = `sqrt(73)` and BC = AD = `sqrt(85)` ...(Opposite sides are equal)
∴ ABCD is a parallelogram.
APPEARS IN
संबंधित प्रश्न
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = -3, y = -6
If P - Q - R and d(P, Q) = 2, d(P, R) = 10, then find d(Q, R).
On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.
d(P, R) + d(R, Q) = d(P, Q)
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
- 25, - 47
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
80, - 85
Show that the following points taken in order to form an isosceles triangle
A(5, 4), B(2, 0), C(−2, 3)
Show that the following points taken in order to form an isosceles triangle
A(6, −4), B(−2, −4), C(2, 10)
Show that the following points taken in order to form an equilateral triangle
`"A"(2, 2), "B"(-2, -2), "C"(-2sqrt(3), 2sqrt(3))`
The point (x, y) is equidistant from the points (3, 4) and (−5, 6). Find a relation between x and y
Find the distance with the help of the number line given below.
d(B, E)
