Match the distance with their respective endpoint coordinates distance coordinate 3.6 units a (-3,4) and (3,4) 4.5 units b (-5,3) and (-5,11) 6 units c (-20-18) and (-22-21) 8 units d (2,4) and origin 15 units e (7,8) and (-2,20)

A = 6 units, B = 8 units, C = 3.6 units, D = 4.5 units, E = 15 units

Step-by-step explanation: A and B can be solved by inspection, as they have a co-ordinate that is the same: A (-3;4) and (3;4) has the same y-coordinate, so the distance between the points can be measured by the difference in their x-coordinates; B (-5;3) and (-5;11) has the same x-coordinates, so the distance can be measured by the difference in their y-coordinates.

The remaining distances need to be solved using the distance formula:

distance =

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: