Find the equation of the line passing through the point ( – 3, 5) an

1.	Find the equation of the line passing through the point ( – 3, 5) and perpendicular to the line joining (2, 5) and ( – 3, 6).
Answer» Given, A line which passes through the point ( – 3,5) and perpendicular to the line joining (2,5) and ( – 3,6) To Find: Find the equation Formula Used: The equation of line is (y – y₁) = m(x – x₁) Explanation: Here, The line passes through the point ( – 3,5 ), Given So, The coordinate (x₁,y₁) = ( – 3,5) Now, The line is perpendicular to the line joining (2,5) and ( – 3,6), We know, The slope of the line with two points is, m = \(\frac{y_2 -y_1}{x_2-x_1}\) So, the slope of line joining (2, 5 ) and ( – 3,6) is = \(\frac{6-5}{-3-2}\) m = \(-\frac{1}{5}\) Therefore, The slope of the required line is, m = \(\frac{1}{Slope \ of \ joining\ line(2,5) and (-3,6)}\) So, m = \(-\frac{1}{\frac{1}{5}}\) m = 5 Now, The equation of straight line is (y – y₁) = m(x – x₁) y – 5 = 5 (x – ( – 3) y – 5 = 5x + 15 5x – y + 20 = 0 Hence, The equation of line is 5x – y + 20 = 0

Find the equation of the line passing through the point ( – 3, 5) and perpendicular to the line joining (2, 5) and ( – 3, 6).

Answer»

Given, A line which passes through the point ( – 3,5) and perpendicular to the line joining (2,5) and ( – 3,6)

To Find: Find the equation

Formula Used: The equation of line is (y – y₁) = m(x – x₁)

Explanation: Here, The line passes through the point ( – 3,5 ), Given

So, The coordinate (x₁,y₁) = ( – 3,5)

Now, The line is perpendicular to the line joining (2,5) and ( – 3,6),

We know, The slope of the line with two points is, m = \(\frac{y_2 -y_1}{x_2-x_1}\)

So, the slope of line joining (2, 5 ) and ( – 3,6) is = \(\frac{6-5}{-3-2}\)

m = \(-\frac{1}{5}\)

Therefore, The slope of the required line is, m = \(\frac{1}{Slope \ of \ joining\ line(2,5) and (-3,6)}\)

So, m = \(-\frac{1}{\frac{1}{5}}\)

m = 5

Now, The equation of straight line is (y – y₁) = m(x – x₁)

y – 5 = 5 (x – ( – 3)

y – 5 = 5x + 15

5x – y + 20 = 0

Hence, The equation of line is 5x – y + 20 = 0