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George decides to walk from his home to Tina’s house down the street. On the way, he stops at the gas station to get some snacks. He begins at (2,3), ends at (9,17), and stops at the gas station at (x,y). If the part to part ratio is 3:4, what is the coordinates of the gas station? (Type out as a coordinate)

Sagot :

Answer:

x = 12 and y = 23

So what we are saying is that the coordinates of Tina’s house down the street is (12,23)

Step-by-step explanation:

 

What this question is actually telling us is that the gas station divides the segment from George’s home to Tina’s house in the ratio 3 to 7; we now want to find the coordinates of Tina’s house which is the end of the line segment.

Mathematically, to get this division, we would have employed the use of the internal division formula;

Coordinates of gas station = (mx2 + nx1)/(m + n) , (my2 + ny1)/(m + n)

m = 3 , n = 1

(x1,y1) = (2,3)

(x2,y2) = (x,y)

So therefore;

(5,9) = 3(x) + 7(2)/3+7) , 3(y) + 7(3)/(3+ 7)

(5,9) = (3x + 14)/10, (3y + 21)/10

Hence;

(3x + 14)/10 = 5

3x + 14 = 10(5)

3x + 14 = 50

3x = 50-14

3x = 36

x = 36/3

x = 12

Also;

(3y + 21)/10 = 9

3y + 21 = 9(10)

3y + 21 = 90

3y = 90-21

3y = 69

y = 69/3

y = 23

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