LINR 3 | Lesson 4 | Making Connections Solutions

  1. Vertices are: A: \((-2,2)\),  B:\((0,0)\) , and C: \( (2,2)\).

Segment AB:  \(m = -1\); segment BC:  \(m = 1\); since the slopes are negative  reciprocals the lines containing the segments are perpendicular so ∠ABC is a right angle.

If you remember the Pythagorean theorem and the Distance Formula you can  also prove that \(AB^2 + BC^2= AC^2\).

  1. Vertices are A: \((1,1)\), B:\((2, 5)\), C: \((6,4)\) and D:\((5,0)\)

Slopes of the sides AB and CD are 4 and slopes of sides AD and BC are \(-\dfrac{1}{4}\). Therefore AB||CD and AD||BC and ABCD is a parallelogram by definition,   Also AB is perpendicular to AD.   The quadrilateral is a rectangle.

You can also show by using the Distance Formula that a pair of opposite sides are congruent and parallel.

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