Math CentralQuandaries & Queries


Subject: coordinate geometry
Name: dusty
Who are you: Student

I am doing a cse in Maths at the AS level. I find some parts straightforward others parts which are a follow on hard.

The question is find an equation for the line perpendicular to:

3x - 4y + 1 = 0 passing through (4,7)

No matter what I do I cannot seem to get the right answer. I maybe missing a part out of the workings. Many thanks

Hi Dusty,

We have two replies for you

I would first put the equation of the line 3x - 4y + 1 = 0 in the form y = mx + b. When you do so the variable m is the slope of the line. A line perpendicular to 3x - 4y + 1 = 0 has slope -1/m . The problem now is to find the equation of the line through (4,7) with slope -1/m .



Hi there,
To find the equation of any line you need two pieces of information:
(i) slope and y-intercept (m and b) or
(ii) slope and a point (m and (x1,y1)) or
(iii) two points ((x1,y1) and (x2, y2))

In your case, slope and a point seems to be the way to go since you already have the point. So how to find the slope you need?

Find the slope of the line whose equation you have been given. Since the two lines are perpendicular, and perpendicular lines have negative reciprocal slopes, you can use this slope to determine the slope you need. For example, if the slope of the line given to you is 2/3, the slope of the perpendicular line would have to be -3/2. In other words, invert the slope and change its sign.

Now you have slope (m) and a point (x1,y1) and can use the formula y-y1=m(x-x1) to determine the equation of the line.

Hope this helps.


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