Thread: lines perpendicular

hey guys, need help with this .. any suggestions with how i should start with question? im not looking for the answer, i want to learn how to do it..thank u

The lines given by ax + by = 3 and cx − 4y = 5 are perpendicular and intersect at (6, 7). Find a, b, and c.

Originally Posted by jvignacio

hey guys, need help with this .. any suggestions with how i should start with question? im not looking for the answer, i want to learn how to do it..thank u

The lines given by ax + by = 3 and cx − 4y = 5 are perpendicular and intersect at (6, 7). Find a, b, and c.

We have the lines and

They are perpendicular and intersect at (6,7)

Recall that the slopes of perpendicular lines are opposite reciprocals of each other.

So we want to find of both lines.

So we see that and

Now, let us evaluate the lines at the intersection point:

-----(1)
--------(2)

We can now solve for c:



Now substitute this value into the derivative.



We see that the negative reciprocal of this slope will give us a slope parallel to the other line. We want these slopes to be equal.

Thus, we must let

We must solve this system of equations in order to find a and b.



I hope this makes sense!

--Chris