Question

How would you answer a coordinate geometry question that involved finding the equation of a line? I want to see what your method would be like compared to my own. There's an example question down there, somewhere, too.

Answer 1

do you have an example we could work with?

Answer 2

I can find one, if you want. I'm just curious as to how other people would do it. Wait a bit, and I'll get one.

Answer 3

cool

Answer 4

The points A and B have coordinates (-2, 10) and (12,3) respectively. The line, L, is perpendicular to AB and intersects the y-axis at the point C (0,-1). The lines AB and L intersect at the point D. Write down the equation of L.

Answer 5

If it helps, I can give you the equation of AB.

Answer 6

I would typically use point-slope form of a line because slope is relatively easy to compute (or given or related to another slope by being parallel / perpendicular), and you only need to know one other point on the line to complete the equation.
\( y - y_1 = m(x-x_1) \) \( m = \dfrac{y_2 - y_1}{x_2 - x_1} \)

So, in your example question, I would first find the line equation for AB. First I need slope, so I compute that using the slope formula. Then plug in the slope and one point (probably (-2,10) for smallest possible numbers) to get the equation.

The line L, I would then use the slope of AB to find the perpendicular slope. We are already given the point C, so that lines up for point-slope form as well (or slope-intercept; they both lead to the same place). After filling in that equation, I would have answered "Write down the equation of L.", so I would be done!

Answer 7

Thank-you! :)

Answer 8

No problem! Always love some coordinate geometry from time to time. :P