Answer:
[tex]29[/tex].
Step-by-step explanation:
All sides of a square are of equal length. Raising the length of one such side to the power of [tex]2[/tex] would give the area of this square.
In this question, finding the length of one side of this square can be a first step towards finding the area of the square.
It is stated that the two coordinates given in this question represent two "consecutive" vertices of this square. In other words, the line segment joining these two points would form one side of this square (instead of a diagonal of the square.)
In a cartesian plane, the length of a line segment between two points [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] is [tex]\sqrt{(x_{1} - x_{0})^{2} + (y_{1} - y_{0})^{2}}[/tex]. The length of the line segment between the two given points in this question (representing one side of this square) would be:
[tex]\sqrt{(7 - 2)^{2} + ((-6) - (-4))^{2}} = \sqrt{29}[/tex].
To find the area of this square, raise the length of one of its sides (like the one between the two given points) to a power of [tex]2[/tex]:
[tex]\begin{aligned} & (\text{area of square}) \\ =\; & (\text{length of one side})^{2} \\ =\; & \left(\sqrt{29}\right)^{2} \\ =\; & 29\end{aligned}[/tex].
In other words, the area of this square would be [tex]29[/tex].
