# math

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Plot the points A(2,2), B(4,6),C(10,-2)Notice that these points are vertices of a right triangle (the angle is 90 degrees).

Find the area of the triangle ABC:

• math -

A(2, 2), B(4, 6), C(10, -2).

(AB)^2 = (4 -2)^2 + (6 -2 )^2,
(AB)^2 = = 4 + 16 = 20.
AB=sqrt20 = sqrt(4*5) = 2*sqrt5 = 4.47.

(BC)^2 = (10 -4)^2 + (-2 -6)^2,
(BC)^2 = 36 + 64 = 100,
BC = sqrt100 = 10.

(AC)^2 = (10 -2)^2 + (-2 -2)^2,
(AC)^2 = 64 + 16 = 80,
AC=sqrt80 = sqrt(16*5) = 4*sqrt5=8.94.

A = AC * AB / 2,
A=4sqrt5 * 2sqrt5/2 = 8 * 5 / 2=20.

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