Question

Find the equation o the line in new position if the line joining two points M(4, 2) and N(5, 3) is rotated about M in anticlockwise
15 degrees.

Answer 1

Answer:

I Don,t know sorry I am today my school homework is taking

Answer 2

Answer:

The equation of the line obtained by rotating the line formed by M(4, 2) and N(5, 3) is y = √3x + 2 - 4√3.

Step-by-step explanation:

Given,

The line is passing through points M(4, 2) and N(5, 3).

To find,

The equation of the line, when the line is rotated anticlockwise 15° about M.

Concept,

The equation of a line with slope m is

y = mx + c

Calculation,

First, we find the slope of the given line M(4, 2) and N(5, 3).

slope of the given line is m = (3 - 2)/(5 - 4)

⇒ m = 1

i.e. tanθ = 1

⇒ θ = 45°

But when the line is rotated by 15° in an anticlockwise fashion about the point M

Then the line makes an angle of (15° + 45°) on the x-axis.

Hence, the slope of the rotated line (m') = tan(60°) = √3

⇒ The equation of a rotated line is:

y = m'x + c

⇒ y = √3x + c.....(1)

Now as the rotated line passes through the point M(4, 2)

Substituting in equation (1) we get:

2 = √3(4) + c

⇒ c = 2 - 4√3

Therefore, the equation of the line obtained by rotating the line formed by M(4, 2) and N(5, 3) is y = √3x + 2 - 4√3.