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(P, R) = d(Q, 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(P, R)
= 8 - 3
= 5
But d(Q, R) = 11
So, d(P, Q) - d(P, R) ≠ d(Q, R)
APPEARS IN
RELATED QUESTIONS
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = -4, y = -5
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = -3, y = -6
Sketch proper figure and write the answer of the following question.
If A- B - C and l(AC) = 11, l(BC) = 6.5, then l(AB) = ?
If P - Q - R and d(P, Q) = 2, d(P, R) = 10, then find d(Q, R).
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)
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.
x + 3, x - 3
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
- 25, - 47
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
80, - 85
If A-B-C and d(A, C) = 17, d(B, C) = 6.5 then d(A, B) = ?
If P-Q-R and d(P, Q) = 3.4, d(Q, R)= 5.7 then d(P, R) = ?
Show that the following points taken in order to form an equilateral triangle
`"A"(2, 2), "B"(-2, -2), "C"(-2sqrt(3), 2sqrt(3))`
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)
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 ______
If the points A(2, 0), B(– 6, 0), C(3, a – 3) lie on the x-axis then the value of a is _____
If (x + 2, 4) = (5, y – 2), then the coordinates (x, y) are _____
Find the distance with the help of the number line given below.
d(B, E)
Find the distance with the help of the number line given below.
d(P, C)
