Question

(c) Show that the line x-y + 2 = 0 and the line jointing the points (4,6) and (10,12)
are parallel to each other.
​

Answer 1

Answer:

ANSWER

Let points be A(−2,6),B(4,8),C(8,12) and D(x,24)

If two lines are perpendicular, then product of their slope is −1

So, Slope of AB× Slope of CD=−1 ......(1)

We know that slope of a line through the points (x

1

,y

1

),(x

2

,y

2

) is m=

x

2

−x

1

y

2

−y

1

Slope of line AB passing through A(−2,6) and B(4,8) is

=

4−(−2)

8−6

=

4+2

8−6

=

6

2

=

3

1

Slope of line CD passing through C(8,12) and D(x,4) is

=

x−8

24−12

=

x−8

12

From (1)

Slope of AB×Slope of CD=−1

⇒

3

1

×

x−8

12

=−1

⇒

x−8

4

=−1

⇒4=−x+8

∴x=4