Construct 8

Construct an analytical geometry problem where it is asked to find the vertices of a triangle ABC:
the vertices of this triangle must be the points A (1,7) B (-5,1) C (5, -11). the said problem should be used the concepts of: distance from a point to a line, ratio of division of a segment by a point and angle between two lines.

a) find the length of all sides of a given triangle ABC

Correct answer:

a =  15.6205
b =  18.4391
c =  8.4853

Step-by-step explanation:

A=(1,7) B=(5,1) C=(5,11)  a=BC a=(CxBx)2+(CyBy)2=(5(5))2+((11)1)2=2 61=15.6205
b=AC b=(CxAx)2+(CyAy)2=(51)2+((11)7)2=2 85=18.4391
b=AB c=(BxAx)2+(ByAy)2=((5)1)2+(17)2=6 2=8.4853

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Tips for 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.
Do you want to convert length units?
See also our trigonometric triangle calculator.
The Pythagorean theorem is the base for the right triangle calculator.

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem: video1   video2

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