# Square

Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.

Result

S =  169

#### Solution:

$a^2 = \Delta x^2 + \Delta y^2 \ \\ \ \\ x_{ 0 } = -9 \ \\ y_{ 0 } = 7 \ \\ x_{ 1 } = -4 \ \\ y_{ 1 } = -5 \ \\ \ \\ a = \sqrt{ (x_{ 0 }-x_{ 1 })^2+(y_{ 0 }-y_{ 1 })^2 } = \sqrt{ ((-9)-(-4))^2+(7-(-5))^2 } = 13 \ \\ \ \\ S = a^2 = 13^2 = 169$

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#### Following knowledge from mathematics are needed to solve this word math problem:

For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc. Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator. Pythagorean theorem is the base for the right triangle calculator.

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