Martin wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. he places parallelogram abcd in the coordinate plane so that a is (0,0), b is (a, 0), c is (a, b), and d is (0,b). what formula can he use to determine the distance from point d to point a?

The formula to find the distance from point d to point a is:

We are given coordinate of the vertices of the parallelogram abcd as:

a(0,0) , b(a,0) , c(a,b) and d(0,b)

We know that the distance between the two points is given by:

Hence,the formula that can be used to determine the distance from point d(0,b) to point a(0,0) is:

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:

26

step-by-step explanation: