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:

a2=Δx2+Δy2  x0=9 y0=7 x1=4 y1=5  a=(x0x1)2+(y0y1)2=((9)(4))2+(7(5))2=13  S=a2=132=169a^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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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.
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