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Question 1078132: The point (-3, -4) divides the line joining A(-6, -7) and B in the ratio 1:3. Find the coordinates of B
please with clear explanation cuz i am slow. thank you
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Look at the x point. A is -6, and the point is -3. This is 3 units toward 0. We keep going 3*3 units in this direction (1:3 ratio) or 9 units. From -3 units towards 0 plus 9 units makes 6 units to the right of 0 (this is the x-value, and we deal left-right with it. The x-value is 6.
The y is -7 and it goes to -4, again 3 units. Again, because it is the same ratio, we add 9 to the y-value of -4 to get +5.
The coordinate is (6,5)
Can check with the distance formula: sqrt (x1-x2)^2+(y1-y2)^2
From A to the point: sqrt (-6-(-3))^2+(-7-(-4))^2=sqrt (9+9)=sqrt(18)
From the point to B: sqrt (-4-5)^2+(-3-6)^2=sqrt (162)
compare sqrt (18) to sqrt (162)
the first is sqrt(9*2) or 3 sqrt (2). The second is sqrt(81*2)=9 sqrt (2)
That is 1:3 ratio.
For medians, rather than doing the distance formula and dividing it in two, just take the average of the x and y points.
For ratio problems like this, deal with each coordinate separately.
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