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?

योग

The coordinate of point A is 1.

Suppose point B is located at a distance of 7 units to the left of point A, whose coordinate is x.

1 > x d(A, B) = 7

∴ 7 = 1 – x

∴ x = 1 – 7

∴ x = - 6

The coordinate of point B is – 6.

Suppose point C is located at a distance of 7 units to the right of point A, whose coordinate is y.

y > 1 d(A, C) = 7

∴ 7 = y – 1

∴ y = 7 + 1

∴ y = 8

The coordinate of point C is 8.

The coordinates of points situated at a distance of 7 units from point A are - 6 and 8.

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Co-ordinates of Points and Distance

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अध्याय 1: Basic Concepts in Geometry - Problem set 1 [पृष्ठ १२]

अध्याय 1 Basic Concepts in Geometry
Problem set 1 | Q 6. | पृष्ठ १२

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 P - Q - R and d(P, Q) = 2, d(P, R) = 10, then find d(Q, R).

Co-ordinates of the pair of points are given below. Hence find the distance between the pair.

- 25, - 47

If P-Q-R and d(P, Q) = 3.4, d(Q, R)= 5.7 then d(P, R) = ?

Find the distance between the following pair of points

(1, 2) and (4, 3)

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 an isosceles triangle

A(5, 4), B(2, 0), C(−2, 3)

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)

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)