Advertisements
Advertisements
Question
On a number line, the co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.
d(R, P) + d(P, Q) = d(R, Q)
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
The co-ordinates of points P, Q and R is 3, −5 and 6 respectively.
We know that 3 > −5
∴ d(P, Q) = 3 − (−5)
∴ d(P, Q) = 3 + 5
∴ d(P, Q) = 8
We know that 6 > −5
∴ d(Q, R) = 6 − (−5)
∴ d(Q, R) = 6 + 5
∴ d(Q, R) = 11
We know that 6 > 3
∴ d(P, R) = 6 − 3
∴ d(P, R) = 3
∴ d(R, P) + d(P, Q)
= 3 + 8
But d(Q, R) = 11
So, d(R, P) + d(P, Q) = d(Q, R)
APPEARS IN
RELATED QUESTIONS
Find the distance with the help of the number line given below.
d (Q, B)
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = -4, y = -5
Sketch proper figure and write the answer of the following question.
If X-Y-Z and l(XZ) = `3sqrt7`, l(XY) = `sqrt7`, then l(YZ) = ?
If P - Q - R and d(P, Q) = 2, d(P, R) = 10, then find d(Q, R).
Co-ordinates of the pair of a point is given below. Hence find the distance between the pair.
3, 6
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
-9, -1
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
0, - 2
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
x + 3, x - 3
Co-ordinate of point A on a number line is 1. What are the co-ordinates of points on the number line which are at a distance of 7 units from A?
Find the distance between the following pair of points
(1, 2) and (4, 3)
Find the distance between the following pair of points
(3, 4) and (−7, 2)
Find the distance between the following pair of points
(a, b) and (c, b)
Determine whether the given set of points are collinear or not
(7, −2), (5, 1), (3, 4)
Show that the following points taken in order to form the vertices of a parallelogram
A(−7, −3), B(5, 10), C(15, 8) and D(3, −5)
Verify that the following points taken in order to form the vertices of a rhombus
A(3, −2), B(7, 6), C(−1, 2) and D(−5, −6)
A(−1, 1), B(1, 3) and C(3, a) are point and if AB = BC, then find ‘a’
Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, −4) and (5, −6)
The distance between the two points (2, 3) and (1, 4) is ______
Find the distance with the help of the number line given below.
d(J, A)
