Given the vertices A(−7,4), B(−1,4), and C(−1,10), find the other vertex that is needed to construct the square.(1 point)
To construct a square, we need to find the point that is equidistant from both A and B, and also equidistant from both B and C.
First, let's find the midpoint of AB. The midpoint formula is
((x1 + x2)/2, (y1 + y2)/2).
The midpoint of AB is ((-7 + -1)/2, (4 + 4)/2) = (-4, 4).
Next, let's find the midpoint of BC. The midpoint formula is
((x1 + x2)/2, (y1 + y2)/2).
The midpoint of BC is ((-1 + -1)/2, (4 + 10)/2) = (-1, 7).
So, the point that is equidistant from both A and B and also equidistant from both B and C is (-1, 7). Therefore, the other vertex of the square is (-1, 7).