Geometry Help

Question

Im having a lot of trouble with this equation. Please explain every step taken to get to the answer...................................... line AB contains points A(-6,-1) and B(1,4). Line CD contains point D(7,2). If angle ABC is congruent to the measure of angle BCD and the measure of angle ABC=90, what is an equation of line CD?

Answer 1

if you draw this out on graph paper you will see that line AB and line CD are parallel

lines AB and CD are both perpendicular to segment BC, therefore they are parallel

parallel lines have the same slope

find the slope of line AB

m=(4-[-1])/1-[-6])

m=5/7

line CD has the same slope 5/7

using the point-slope form

y=mx+b

y=(5/7)x+b

using point D(7,2)

2=(5/7)(7)+b

2=5+b

b=2-5

b=-3

the equation of the line CD is y=(5/7)x-3

Answer 2

Victoria,

Angles ABC & BCD are congruent and that they are 90° each means lines AB & CD are parallel. 

(1) This implies that the equation passing through points C and D has the same slope as that of the equation containing A & B.

(2) Slope of AB, m(AB)= (4--1)/(1--6)=5/7

(3) => the slope of the equation containing points C & D = m(CD)= [correction] m(AB)=5/7 -1/m(AB)=-7/5

(3) The equation of the line containing points C & D = y(CD)=mx+b=[correction]5/7+b, or 2=5/7(7)+b.=>b=-3

-7/5x+b. Or, 7=-7/5(2)+b =>b=40

∴ equation passing through DC is y=-7/5x+40

 

y=5/7x-3

I hope this helps