Division of a line segment. Please give me the solution and the graph.
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The ratio 2:3 means that the segment is to be divided by 5 and the two parts of the segment will be 2/5 and 3/5. The question doesn't say from which end to measure the division, so we'll assume that we need the point 2/5 from the leftmost end of the segment. The easiest way is to divide the difference between the x and y coordinates by 5, then multiply each by 2 to get the coordinates of the division. 6-(-5)=11 and 2/5 of this x coordinate is 4.4; -2-(-4)=2 and 2/5 of this y coordinate 2 is 0.8, so the division point is (-5+4.4,-4+0.8)=(-0.6,-3.2).

(To get the equation of the graph y=mx+b, we first need to work out the slope, m=2/11 being the difference of the y coordinates divided by the difference of the x coordinates. So y=2x/11+b: -4=2*(-5)/11+b, putting in (-5,-4); b=-4+10/11=-34/11, so y=2x/11-34/11 or 11y=2x-34. Check: put in x=6: 11y=12-34=-22, so y=-2 so (6,-2) is also on the line. Let's make sure (-0.6,-3.2) is on the line: 11y=-1.2-34=-3.2, which checks out.)

To draw the graph, just draw a line through (-5,-4) and (6,-2). If you just join the two points, you will have the line segment. Mark the division point on the line at (-0.6,-3.2).


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