Advertisements
Advertisements
प्रश्न
Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.
उत्तर
AB = `sqrt((1 - 5)^2 + (5 - 6)^2) = sqrt(16 +1) = sqrt(17)`
BC = `sqrt((2 - 1)^2 + (1 - 5)^2) = sqrt(1+16) = sqrt(17)`
CD = = `sqrt((6 - 2)^2 + (2 - 1)^2) = sqrt(16 + 1) = sqrt(17)`
DA = = `sqrt((5 - 6)^2 + (6 - 2)^2) = sqrt(1+16) = sqrt(17)`
AC = = `sqrt((2 - 5)^2 + (1 - 6)^2) = sqrt(9+25) = sqrt(34)`
BD = = `sqrt((6 - 1)^2 + (2 - 5)^2) = sqrt(25+9) = sqrt(34)`
Since, AB = BC = CD = DA and AC = BD,
A, B, C and D are the vertices of a square.
APPEARS IN
संबंधित प्रश्न
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
Find the distance between the following pairs of points:
(−5, 7), (−1, 3)
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.
If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.
Find the distance between the points
A(-6,-4) and B(9,-12)
The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?
Find the distance between the following pair of points.
R(0, -3), S(0, `5/2`)
Find the distance between the following pair of points.
L(5, –8), M(–7, –3)
Find the distance of a point (13 , -9) from another point on the line y = 0 whose abscissa is 1.
Prove that the following set of point is collinear :
(5 , 1),(3 , 2),(1 , 3)
Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.
ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.
From the given number line, find d(A, B):
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.
Find the distance of the following points from origin.
(a cos θ, a sin θ).
The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?
