Which of these points lies on the straight line joining the points (4,4) and (20,12)? A. (5,5) B. (6,6) C. (10,7) D.(14,8)Explain how you...

First, we'll determine the equation of the line that
passing through the given points (4,4) and (20,12).

(20 -
4)/(x - 4) = (12 - 4)/(y - 4)

16/(x - 4) = 8/(y -
4)

We'll divide by 8:

2/(x -
4) = 1/(y - 4)

We'll cross multiply and we'll
get:

x - 4 = 2y - 8

We'll keep
2y to the right side, moving -8 to the left:

x - 4 + 8 =
2y

2y = x + 4

y = x/2 +
2

Since we know now the equation of the line, we could tell
what other point lies on this line, replacing the coordinates x and y by the values of
the coordinates of the points.

We'll check if the point
(5,5) is on the line:

5 = 5/2 +
2

5 = (5+4)/2

5 = 9/2
impossible

Since LHS is different from RHS, the point is
not located on this line, y = x/2 + 2.

We'll verify the
point (6,6):

6 = 6/2 + 2

6 = 3
+ 2

6 = 5 impossible

As we can
see, (6,6) is not located on the line y = x/2 + 2.

We'll
check for (10,7):

7 = 10/2 +
2

7 = 5 + 2

7 =
7

The point (10,7) lies on the line y = x/2 +
2.

We'll check (14,8):

8 =
14/2 + 2

8 = 7 + 2

8 = 9
impossible

The point (14,8) is not on the line y = x/2 +
2.

We found the option C. (10 , 7) is
convenient in the given circumstances.