Advertisements
Advertisements
प्रश्न
Show that the following points are the vertices of a square:
A (6,2), B(2,1), C(1,5) and D(5,6)
उत्तर
The given points are A (6,2), B(2,1), C(1,5) and D(5,6)
`AB = sqrt((2-6)^2 +(1-2)^2) = sqrt((-4)^2 +(-1)^2) = sqrt(16+1) = sqrt(17) units`
`BC = sqrt((1-2)^2 +(5-1)^2) = sqrt((-1)^2 +(-4)^2) = sqrt(1+16) = sqrt(17) units`
`CD = sqrt((5-1)^2 +(6-5)^2) = sqrt ((4)^2+(1)^2) = sqrt(16+1) = sqrt(17) units`
`DA = sqrt((5-6)^2 +(6-2)^2 )= sqrt((1)^2 +(4)^2) = sqrt(1+16) = sqrt(17) units`
Therefore, AB =BC =CD =DA = 17 units
Also, `AC = sqrt((1-6)^2 +(5-2)^2 ) = sqrt((-5)^2 +(3)^2) = sqrt(25+9) = sqrt(34) units`
`BD = sqrt((5-2)^2 +(6-1)^2) = sqrt((3)^2+(5)^2) = sqrt(9+25) = sqrt(34) units`
Thus, diagonal AC = diagonal BD
Therefore, the given points from a square.
APPEARS IN
संबंधित प्रश्न
How will you describe the position of a table lamp on your study table to another person?
The base PQ of two equilateral triangles PQR and PQR' with side 2a lies along y-axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R' of the triangles.
The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.
Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and(1, 2) meet
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
The line joining the points (2, 1) and (5, -8) is trisected at the points P and Q. If point P lies on the line 2x - y + k = 0. Find the value of k.
Show that the following points are the vertices of a square:
(i) A (3,2), B(0,5), C(-3,2) and D(0,-1)
Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.
ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of one its diagonal.
If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k,5), find the value of k.
Find the centroid of ΔABC whose vertices are A(2,2) , B (-4,-4) and C (5,-8).
The measure of the angle between the coordinate axes is
Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?
If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=
The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______
Point (–10, 0) lies ______.
The distance of the point (–1, 7) from x-axis is ______.
