Advertisements
Advertisements
Question
Prove that the points P (0, -4), Q (6, 2), R (3, 5) and S (-3, -1) are the vertices of a rectangle PQRS.
Advertisements
Solution
PQ = `sqrt((6 - 0)^2 + (2 + 4)^2) = 6sqrt(2)"units"`
QR = `sqrt((6 -3)^2 + (2 - 5)^2) = 3sqrt(2)"units"`
RS = `sqrt((3 +3)^2 + (5 + 1)^2) = 6sqrt(2)"units"`
PS = `sqrt((-3 - 0)^2 + (-1 + 4)^2) = 3sqrt(2)"units"`
PR = `sqrt((3 - 0)^2 + (5 + 4)^2) = 3sqrt(10)"units"`
QS = `sqrt((6 +3)^2 + (2 + 1)^2) = 3sqrt(10)"units"`
∵ PQ = RS and QR = PS,
Also PR = QS
∴ PQRS is a rectangle.
APPEARS IN
RELATED QUESTIONS
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius.
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)
If a≠b≠0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.
Using the distance formula, show that the given points are collinear:
(-1, -1), (2, 3) and (8, 11)
Determine whether the points are collinear.
A(1, −3), B(2, −5), C(−4, 7)
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the ordinate of point P.
The distance between the points A(0, 6) and B(0, -2) is ______.
The distance between the points (0, 5) and (–3, 1) is ______.
