The coordinates of the midpoint of ab are (2,4),
and the coordinates of point b are (3,7). what are
the coordinates of point a? [the use of the
accompanying grid is optional.]

You can use the midpoint formula.

Method:

MAB = (Ax+Bx)/2 ; (Ay+By)/2

Substitute in what you have:

(2;4) = (Ax+3)/2 ; (Ay+7)/2

Because we know the x coordinate of the midpoint, we can assume that:

2 = (Ax+3)/2

And now solve for Ax:

4 = Ax+3
Ax = 1

Because we know the y coordinate of the midpoint, we can assume that:

4 = (Ay+7)/2

And now solve for Ay:
8 = Ay+7
Ay = 1

Therefore A(1;1)