How can I find the midpoint of the line seven times joining the points R(3,1) and S(-4,2) ?

Question

My new school has a summer packet and my old teacher never taught me it so it would be amazing if someone could please explain how to do it.

Answer 1

What do you mean by "the line seven times joining the points R(3,1) and S(-4,2)" ? There is a single straight line joining the 2 given points.  If you want the coordinates of the mid point between points (x1,y1) and (x2,y2), they are

 

x_mid = (x1 + x2) / 2

y_mid = (y1 + y2) / 2

 

In this case,

 

x_mid = (3 - 4) / 2 = -1/2

y_mid = (1 + 2) /2 = 3/2

Answer 2

Is this the entire problem, word for word? Because there's a midpoint of the line - that can be figured out - and a solution if the question wants to know the midpoint of a line 7 times as long as the line joining those points, and there's a solution if you want the midpoint of the original line times 7...The question needs to say "7 times [what]. This question isn't commutative as stated so it needs to be re-formed. In fact, this question as written asks about a line that joins R and S 7 times...which is a pretty weird line, and I'm sure is not what they meant.

 

I can guess what they thought they'd asked and that would be a line 7 times the length of the line from R to S (which I'm going to assume you know how to figure out) and then figure out where the midpoint of that longer line would fall on the graph.

 

I can also tell you that whatever they meant, the question is supposed to teach/test your ability to work with dimensions on graphs.