On a number line, suppose the coordinate of A is 0, and AR = 9. What are the possible coordinates of the midpoint of AR?

Given:

On a number line, suppose the coordinate of A is 0, and AR = 9.

To find:

The possible coordinates of the midpoint of AR.

Solution:

Coordinate of A is 0, and AR = 9.

It means the distance between point A and R is 9 units. It means, point R can be either left side or right side of A. So, location of point R can be either -9 or 9.

If coordinate of R is -9, then midpoint of AR is

If coordinate of R is 9, then midpoint of AR is

Therefore, the possible coordinates of the midpoint of AR are -4.5 and 4.5.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is