We could simply plot the other sets of points and find out which set forms a rectangle with the two given points, (-3,2), and (1,2).
However, that seems either too difficult or too easy, such that no one offered a solution that way. I will still leave that option open for anyone who wishes to try it.
The problem is very much suited for a solution by look at the numbers, in other words, by inspection.
The given (fixed) points are (-3,2) and (1,2), they both lie on the horizontal line y=2. From the properties of a rectangle, the other two points must be parallel, hence they should also lie on a horizontal line.
Looking at the 4 possible options, we notice that all options have the points lie on the horizontal line y=5, evidenced by the fact that all points have a y-coordinate of y=5.
Thus our only job is to find points such that they line up vertically with the two given points (-3,2), (1,2). In other words, the other two points must have the coordinates (-3, 5), (1,5) which match the x-coordinates of the given points.
So the above is the method by inspection which can be applied given the two given points lie on a horizontal (or vertical) line.
1.x2x +x.4x7 5.036 (sorry the underline function is no longer available)
In the thousandth column we have x +7 and we wind up with a 6 in that column. Since 7 is already more than 6 that means the only number that will work is 9 and there will be a carry of one into the hundredths place.
1.x29 +x.4x7 5.036
Now let's look at the tenths column. 2 becomes 3 in the answer and there was a carry of 1 from the thousandths so the other number must be a zero 1.x29 + x.407 5.036 Now I need a number that goes with 4 and puts a zero in the answer. That number has to be 6 and does cause a carry of one into the ones place
1.629 +x.407 5.036
Finally (remembering there is a carry of one in the ones place) I have two (1 + 1 carried) toward my five in the answer. I need three more.
Average of 5 games = 13 Total of 5 games = 13 x 5 = 65
Average of 6 games = 17 Total of 6 games = 102
6th game = 102 - 65 = 37
--------------------------------------------------------------------- Answer: Her score for the 6th game as 37. ---------------------------------------------------------------------