Question

Line segments, AB, BC, CD, DA create the quadrilateral graphed on the coordinate grid above. The equations for two of the four line segments are given below. Use the equations of the line segments to answer the questions that follow. AB: y = -x + 1 1

Answer 1

Given the equations of the side length as shown;

AB y = 1/3 x + 1

CD = y = -3x+11

Before we determine whether they are parallel or perpendicular, we must first know that;

Two parallel lines have the same slope i.e Mab = Mcd

For two lines to be perpendicular then the product of the slopes must give -1 i.e MabMcd = -1

Comapring both equations with the general equation of a line y = mx+c;

For line AB: y = 1/3 x + 1

Mab = 1/3

For line CD: y = -3x+11

Mcd = -3

Taking the product of the slope;

MabMcd = 1/3 * -3

MabMcd = -1

Is AB perpendicular or parallel to CD? Since the product of their slope gives -1, hence the lines AB and CD are PERPENDICULAR to each other.