Question

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 ?

Answer 1

The co-ordinates of point A on the number line is 1. Now, there will be two points, one on the left of point A and the other on the right of point A on the number line which are at a distance of 7 units from point A.
Let the point C is on the right of point A and point B is on the left of point A each at a distance of 7 units from point A.
The co-ordinate of point C will be larger and co-ordinate of point B will be smaller in comparison to the co-ordinate of point A.
Now, d(A, C) = 7
So, co-ordinate of C − co-ordinate of A = 7
∴ co-ordinate of C = 7 + co-ordinate of A = 7 + 1= 8
Also, d(B, A) = 7
So, co-ordinate of A − co-ordinate of B = 7
∴ co-ordinate of B = co-ordinate of A − 7 = 1 − 7 = −6

Hence, the co-ordinates of the required points on the number line which are at a distance of 7 units from the point A are 8 and −6.