Vertices of a right triangle

Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.

Correct answer:

d =  0

Step-by-step explanation:

x1=2 y1=1 x2=4 y2=0 x3=5 y3=7  a=(x1−x2)2+(y1−y2)2=(2−4)2+(1−0)2=5≐2.2361  b=(x1−x3)2+(y1−y3)2=(2−5)2+(1−7)2=3 5≐6.7082  c=(x2−x3)2+(y2−y3)2=(4−5)2+(0−7)2=5 2≐7.0711  c2=a2+b2? d=c2−a2−b2=7.07112−2.23612−6.70822=0

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Tips to related online calculators
Line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
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Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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