Question

Igor believes the slope of AC is greater than the slope DF, while Keenan believes the two slopes are equal. Who do you agree with?
Please help

Justify your answer

Answer 1

Answer:

Both slopes are equal

There are multiple ways to prove this point. I'll tell 2.

1) Inclination of lines

Inclination basically refers to the angle subtended by a line with respect to the x axis.

And since DF actually lies on AC, we can say that both are equally inclined to the x axis, and hence both have the same slope.

2) Find slope for AC and DF

Formula of slope = (y2-y1)/(x2-x1)

AC : A(x1,y1) = (5,7), and C(x2,y2) = (-7,-2)

So slope of AC = (-2 -7)/(-7 -5) = -9/-12 = 3/4

DF : D(x1,y1) = (1,4), and F(x2,y2) = (-3,1)

So slope of DF = (1-4)/(-3-1) = -3/-4 = 3/4

Hence, Slope of AC = DF = 3/4