Advertisements
Advertisements
प्रश्न
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)
पर्याय
True
False
Advertisements
उत्तर
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
संबंधित प्रश्न
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = 4, y = - 8
Find d(A, B), if co-ordinates of A and B are -2 and 5 respectively.
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)
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-ordinates of the pair of points are given below. Hence find the distance between the pair.
80, - 85
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 isosceles triangle
A(6, −4), B(−2, −4), C(2, 10)
Show that the following points taken in order to form an equilateral triangle
`"A"(2, 2), "B"(-2, -2), "C"(-2sqrt(3), 2sqrt(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)
The point (x, y) is equidistant from the points (3, 4) and (−5, 6). Find a relation between x and y
Let A(2, 3) and B(2, −4) be two points. If P lies on the x-axis, such that AP = `3/7` AB, find the coordinates of P.
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 (x + 2, 4) = (5, y – 2), then the coordinates (x, y) are _____
The distance between the point (5, −1) and the origin is _________
