MATHS-IB
STRAIGHT LINES
1. Write the equation of the reflection of the line x=1, in the y-1 axis.
Answers
Answer:
The equation of the line x = 1 will be :
x = -1 as it gets reflected through y axis
==> x + 1 = 0
This is the equation
Solution:
A straight line can be represented in various forms as illustrated in the chart given below:
A straight line can be represented in various forms
Now, we express the given line i.e. 3x – 4y + 5 = 0 in the various forms one by one:
Slope Intercept Form
y = 3/4 x + 5/4
where, m = slope = 3/4
c = 5/4 (y – intercept)
Intercept Form
We can write the given line as 3x – 4y = –5
⇒ 3x/–5 + 4y/5 = 1
x/–5/3 + y/5/4 = 1 (intercept form)
x – intercept = –5/3
y – intercept = 5/4
Point – Slope Form
Let x = 1, then y = 3/4 + 5/4 = 2
y – 2 = 3/4 (x – 1)
Parametric Form
x–1/cos θ = r, where tan θ = 3/4
⇒ x–1/4/5 = y–2/3/5 = r
Normal Form
3x – 4y = – 5
–3x + 4y = 5
Dividing by ((–3)2 + 4)½
⇒ –3/5 x + 4/5 y = 5/5 = 1
⇒ x cos α + y sin α = p, p > 0
Where cos α = –3/5, sin α = 4/5, p = 1