Equation of line passing through (1, 1) and making an angle of (3pi)/4 is
Answers
Answer:
5 pie squared
Step-by-step explanation:
nothing
Given:
A straight line passes through (1,1) and makes an angle of (3π/4) with the +ve x-axis.
To Find:
The equation of the straight line.
Solution:
1. It is given that a line is passing through (1,1) and it makes an angle of (3π/4) with the positive X-axis.
2. According to the properties of straight lines,
- The equation of a line having slope m and an intercept c is given by the formula, y = mx + c where m is the slope of the line and c is a constant.
- The Slope of the line m is also equal to tanx. (where x is the angle made by the line with the +ve x-axis.)
3. The given angle is (3π/4), Therefore the value of m will be,
=> m = tanx ,
=> m = tan(3π/4),
=> m = -1.
4. Now, the given equation reduces to y = -1(x) + c.
5. Since the line passes through (1,1), Hence, (1,1) should satisfy the above equation.
On substitution we get,
=> 1 = -1 + c,
=> c = 2.
5. On substituting the value of c, the equation of the given line reduces to
y = -x + 2.
Therefore the equation of the line is x + y = 2.