Advertisements
Advertisements
Question
Show that the following points are the vertices of a square:
A (6,2), B(2,1), C(1,5) and D(5,6)
Advertisements
Solution
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
RELATED QUESTIONS
Prove that the points (−2, 5), (0, 1) and (2, −3) are collinear.
If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.
Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).
In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at A(3, 1), B(6, 4), and C(8, 6). Do you think they are seated in a line?
Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by y-axis. Also, find the coordinates of the point of division in each case.
Determine the ratio in which the point (-6, a) divides the join of A (-3, 1) and B (-8, 9). Also, find the value of a.
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
In what ratio does the line x - y - 2 = 0 divide the line segment joining the points A (3, 1) and B (8, 9)?
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k.
A point whose abscissa and ordinate are 2 and −5 respectively, lies in
The abscissa of any point on y-axis is
If A(3, y) is equidistant from points P(8, −3) and Q(7, 6), find the value of y and find the distance AQ.
What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4)?
If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
If the points(x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =
The point on the x-axis which is equidistant from points (−1, 0) and (5, 0) is
Point (0, –7) lies ______.
A point both of whose coordinates are negative will lie in ______.
