Advertisements
Advertisements
Question
On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.
d(P, Q) + d(Q, R) = d(P, R)
Options
True
False
Advertisements
Solution
This statement is False.
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(P, Q) + d(Q, R)
= 8 + 11
= 19
But d(P, R) = 3
So, d(P, Q) + d(Q, R) ≠ d(P, 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 = -3, y = -6
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = 4, y = - 8
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) = ?
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)
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.
- 25, - 47
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)
Show that the following points taken in order to form an equilateral triangle
`"A"(sqrt(3), 2), "B"(0, 1), "C"(0, 3)`
Show that the following points taken in order to form the vertices of a parallelogram
A(−3, 1), B(−6, −7), C(3, −9) and D(6, −1)
Verify that the following points taken in order to form the vertices of a rhombus
A(1, 1), B(2, 1), C(2, 2) and D(1, 2)
A(−1, 1), B(1, 3) and C(3, a) are point and if AB = BC, then find ‘a’
The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, What are the coordinates of A?
Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, −4) and (5, −6)
If the points A(2, 0), B(– 6, 0), C(3, a – 3) lie on the x-axis then the value of a is _____
Find the distance with the help of the number line given below.
d(P, C)
