Question

The x coordinate of a point on the slanted (blue) line is 3:

i. What it its y coordinates?

ii. What is the slope of the line?

iii. Write the equation of the line.

Answer 1

As we get a right triangle on joining die three points’, with angles 30 : 60: 90 and ratio of their sides 1 : √3: 2

i. y coordinate is \(2\sqrt{3}\)

ii. slope of line = \(\frac{2\sqrt{3}-0}{3-1}\) = \(\frac{2\sqrt{3}}{2}\) = \(\sqrt{3}\)

= \(\frac{y-0}{x-1}\) = \(\frac{2\sqrt{3}-0}{3-1}\)

\(\frac{y}{x-1}\) = \(\frac{2\sqrt{3}}{2}=\sqrt{3}\)

\(y=\sqrt{3}\) (x-1)