Dividing line segments

- [Instructor] We're told point A is at negative one comma four and point C is at four common negative six. Find the coordinates of point B on segment, line segment AC such that the ratio of AB to AC is three to five. So pause this video and see if you can figure that out. All right, now let's work through this together and to help us visualize, let's plot these points. So first, let us plot point A which is at negative one comma four. So negative one comma one, two, three, four so that right over there is point A and then let's think about point C which is at four common negative six. So one, two, three, four, comma negative six, negative one, negative two, negative three, negative four, negative five, negative six, just like that and so the segment AC, I get my ruler tool out here. Segment AC is going to look like that and the ratio between the distance of A to B and A to C is three to five or another way to think about it is B is going to be three fifths along the way from A to C. Now the way that I think about it is in order to be three fifths along the way from A to C you have to be three fifths along the way in the X direction and three fifths along the way in the Y direction. So let's think about the X direction first. We are going from X equals negative one to X equals four to go from this point to that point. Our change in X is one, two, three, four, five and so if we wanna go three fifths of that, we went a total of five, three fifths of that is going just three. So that is going to be B is X coordinate and then we can look on the Y coordinate side. To go from A to C, we are going from four to negative six so we're going down by one, two, three, four, five, six, seven, eight, nine, 10 and so three fifths of 10 would be six. So B's coordinate is going to be one, two, three, four, five, six down. So just like that, we were able to figure out the X and the Y coordinates for point B, which would be right over here and you could look at this directly and say, look, B is going to be have the coordinates. This looks like this is two comma negative two which we were able to do the graph paper. So another way you could think about it even algebraically is the coordinates of B, we could think about it as starting with the coordinates of A so negative one comma four, but we're gonna move three fifths along the way in each of these dimensions towards C. So it's going to be plus three fifths times how far we've gone in the extraction. So in the extraction to go from A to C, you were going from negative one to four and so that distance is four minus negative one and this of course is going to be equal to five and then on the Y dimension, this is going to be our A's Y coordinate plus three fifths times the distance that we travel in the Y direction and here we're going from four to negative six. So we say negative six minus four, that is negative 10 and so the coordinates of B are gonna be negative one plus three fifths times five is going to be plus three and then four plus three fifths times negative 10, well, three three fifths negative 10 is negative six. and so that gets us two comma negative two and we are done, which is exactly what we got right over there.