Advertisements
Advertisements
प्रश्न
Show that the following points are the vertices of a square:
A (0,-2), B(3,1), C(0,4) and D(-3,1)
उत्तर
The given points are A (0,-2), B(3,1), C(0,4) and D(-3,1)
`AB = sqrt ((3-0)^2 +(1+2)^2) = sqrt((3)^2+(3)^2) = sqrt(9+9) = sqrt(18) = 3sqrt(2) units`
`BC = sqrt ((0-3)^2 +(4-1)^2) = sqrt((-3)^2 +(3)^2) = sqrt(9+9) = sqrt(18) = 3 sqrt(2) units`
`CD = sqrt((-3-0)^2 + (1-4)^2) = sqrt((-3)^2 +(-3)^2 ) = sqrt(9+9) = sqrt(18) = 3 sqrt(2) units`
`DA = sqrt((-3-0)^2 +(1+2)^2) = sqrt((-3)^2 +(3)^2) = sqrt(9+9) = sqrt(18) = 3 sqrt(2) units`
Therefore, `AB = BC = CD = DA = 3 sqrt(2) units`
Also ,
`AC= sqrt((0-0)^2 + (4+2)^2) = sqrt((0)^2 +(6)^2 ) = sqrt(36) = 6 units`
`BD = sqrt((-3-3)^2 +(1-1)^2) = sqrt((-6)^2 +(0)^2) = sqrt(36) =6 units`
Thus, diagonal AC = diagonal BD
Therefore, the given points from a square.
APPEARS IN
संबंधित प्रश्न
On which axis do the following points lie?
Q(0, -2)
Find a point on y-axis which is equidistant from the points (5, -2) and (-3, 2).
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in five equal parts. Find the coordinates of the points P,Q and R
If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k,5), find the value of k.
If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is
Find the value of k, if the points A (8, 1) B(3, −4) and C(2, k) are collinear.
If three points (x1, y1) (x2, y2), (x3, y3) lie on the same line, prove that \[\frac{y_2 - y_3}{x_2 x_3} + \frac{y_3 - y_1}{x_3 x_1} + \frac{y_1 - y_2}{x_1 x_2} = 0\]
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
Find the area of triangle with vertices ( a, b+c) , (b, c+a) and (c, a+b).
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio.
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
In which quadrant does the point (-4, -3) lie?
What is the nature of the line which includes the points (-5, 5), (6, 5), (-3, 5), (0, 5)?
Points (1, – 1), (2, – 2), (4, – 5), (– 3, – 4) ______.
Point (3, 0) lies in the first quadrant.
The distance of the point (–6, 8) from x-axis is ______.
