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
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = 1, y = 7
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = 6, y = - 2
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = - 3, y = 7
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).
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.
- 25, - 47
Co-ordinate of point P on a number line is - 7. Find the co-ordinates of points on the number line which are at a distance of 8 units from point P.
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?
Show that the following points taken in order to form an equilateral triangle
`"A"(2, 2), "B"(-2, -2), "C"(-2sqrt(3), 2sqrt(3))`
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?
The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.
The point whose ordinate is 4 and which lies on the y-axis 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(J, A)
Find the distance with the help of the number line given below.
d(O, E)
