Question

write the angle made by the line joining P(2,4) and Q(4,6) with x-axis.​

Answer 1

Answer:

Given two points (x1,y1) and (x2,y2)

The slope of that line in Cartesian plane is given as

Slope = y2-y1/x2-x1 = tan theta where theta is the angle of the line with the positive side of the x-axis.

So,

Slope = 6-4/4-2 = 1

So,

tan theta = 1

or,

theta = 45° which is the angle made by the line joining points P and Q with positive axis of x.

Answer 2

The angle made by the line joining P(2,4) and Q(4,6) with x-axis is equal to 45⁰.

• If a is the angle made by any line with the x-axis, them tan(a) is equal to the slope of the line.
• The slope of the line joining two points (x1,y1) and (x2,y2) is equal to (y2-y1)/(x2-x1).
• The slope of the line PQ is equal to 1.
• Hence tan(a) = 1 ⇒ a = 45⁰.