Q. 7

# Show that the points P(2, 3, 5), Q(-4, 7, -7), R(-2, 1, -10) and S(4, -3, 2) are the vertices of a rectangle.

Answer :

To prove: Points P, Q, R, S forms rectangle.

Formula:

The distance between two points (x_{1},y_{1},z_{1}) and (x_{2},y_{2},z_{2}) is given by

D=

Here,

(x_{1},y_{1},z_{1})= (2, 3, 5)

(x_{2},y_{2},z_{2})= (-4, 7, -7)

(x_{3},y_{3},z_{3})= (-2, 1, -10)

(x_{4},y_{4},z_{4})= (4, -3, 2)

Length PQ =

=

=

=

=

Length QR =

=

=

=

=

Length RS =

=

=

=

=

Length PS =

=

=

=

=

Length PR =

=

=

=

=

Length QS =

=

=

=

=

Here, PQ = RS which are opposite sides of polygon.

QR = PS which are opposite sides of polygon.

Also the diagonals PR = QS.

Hence, the polygon is a rectangle.

Rate this question :

Determine the point on yz-plane which is equidistant from points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1).

RD Sharma - MathematicsThe length of the perpendicular drawn from the point P(a, b, c) from z-axis is

RD Sharma - MathematicsLet (3, 4, -1) and (-1, 2, 3) be the endpoints of a diameter of a sphere. Then, the radius of the sphere is equal to

RD Sharma - MathematicsThe length of the perpendicular drawn from the point P(3, 4, 5) on the y-axis is

RD Sharma - MathematicsIf P (0, 1, 2), Q(4, -2, 1) and O(0, 0, 0) are three points, then ∠POQ =

RD Sharma - MathematicsShow that the triangle ABC with vertices A (0, 4, 1), B (2, 3, – 1) and C (4, 5, 0) is right angled.

Mathematics - ExemplarWrite the length of the perpendicular drawn from the point P(3, 5, 12) on the x-axis.

RD Sharma - MathematicsIf the distance between the points P(a, 2, 1) and Q(1, -1, 1) is 5 units, find the value of a.

RD Sharma - MathematicsFind the point on y-axis which is at a distance of units from the point (1, 2, 3).

RD Sharma - MathematicsFind the point on x-axis which is equidistant from the points A(3, 2, 2) and B(5, 5, 4).

RD Sharma - Mathematics