# 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 work it out

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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.