The points A,Band C are (9,8), (12,4), (4,2) respectively Find the gradient of the line theough A and B and Find the equation of the line C which is Parallel to AB
Answers
Step-by-step explanation:
The general case
We can obtain a formula for the length of any interval. Suppose that P(x1, y1) and Q(x2, y2) are two points.
Form the right-angled triangle PQX, where X is the point (x2, y1),
PX = x2 − x1 or x1 − x2 and QX = y2 − y1 or y1 − y2
depending on the positions of P and Q.
By Pythagoras’ theorem:
PQ2 = PX2 + QX2
= (x2 − x1)2 + (y2 − y1)2
Therefore PQ = QP =
Note that (x2 − x1)2 is the same as (x1 − x1)2 and therefore it doesn’t matter whether we go from P to Q or from Q to P − the result is the same.
EXAMPLE
Find the distance between the points A(−4, −3) and B(5, 7).
SOLUTION
In this case, x1 = −4, x2 = 5, y1 = −3 and y2 = 7.
AB2 = (x2 − x1)2 + (y2 − y1)2
= (5 − (−4))2 + (7 − (−3))2
= 92 + 102
= 181
Thus, AB =
Note that we could have chosen x1 = 5, x2 = −4, y1 = 7 and y2 = −3 and still obtained the same result. As long as (x1, y1) refers to one point and (x2, y2) the other point, it does not matter which one is which.