geomitry, graphs

Dom:

are the lines (3,4)-(7,7)AB and (0,0)-(-6,8) parallel, perpendicular, or neather?

Let's first draw them on graph paper;

Knipsel20.PNG

We can see that they are obviously not parallel, but they can be perpendicular.

Let check what the gradients of both lines are,

for the first line, if x increases with 4, y increases with 3, so if x increases with 1 y increases with 3/4.

for the second line, if x increases with 3, y decreases with 4, so if x increases with 1 y decreases with 4/3.

So the gradient of line 1 is 3/4 and the gradient of line 2 is -4/3

The rule is that if line B is perpendicular to line A, then gradient(B) = -1/gradient(A) and similarly gradient(A) = -1/gradient(B)

Why? It's a little much to explain but you can find the full explanation here; http://www.mathsisfun.com/algebra/line-parallel-perpendicular.html

Since -1/(3/4) = -4/3 and -1/-(4/3) = 3/4 the lines are perpendicular.

Reinout

Dom:

are the lines A(3,4)B(7,7) and C(0,0)D(-6,8) parallel, perpendicular, or neather?

the formula for gradient is (y ₂-y ₁) / (x ₂-x ₁)

so the gradient of AB is (7-4) / (7-3) = 3/4
and
the gradient of CD is (8-0) / (-6-0) = 8/-6 = -4/3

Now the gradients are different so the lines cannot be parallel.
but
3/4 * -4/3 = -1
and this means that the lines are perpendicular.
If two gradients multiply to give -1 then the lines are perpendicular
And, if this is the case then one gradient is the negative reciprocal of the other one.