Answer:
a) Slope of line 1 = (2/3)
b) Slope of line 2 = (-3/2)
c) Two lines are perpendicular.
Step-by-step explanation:
Here, let the points of line 1 are A(1,0) and B(7,4)
Let the points of line 2 are A(7,0) and B(3,6)
Now for any two points, the slope m of the line is given as :
[tex]m = \frac{y_2 - y_1}{x_2-x_1}[/tex]
⇒Slope of the line AB = [tex]m1 =( \frac{4-0}{7-1}) = \frac{4}{6} = \frac{2}{3}[/tex]
or, m1 = 2/3
and Slope of the line PQ = [tex]m2 =( \frac{6-0}{3-7}) = -\frac{6}{4} = -\frac{3}{2}[/tex]
or, m2 = -3/2
Now, TWO LINERS ARE SAID TO BE PERPENDICULAR if
m1 x m2 = -1 :with heir respective slope m1 and m2
Here, [tex]m1 \times m2 = \frac{2}{3} \times \frac{-3}{2} = -1[/tex]
⇒ SLOPE OF AB x SLOPE OF PQ = -1
Hence, Line AB is perpendicular to the line PQ.
