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Question 980006: If A and B are two points on a plane with coordinates of (6, -4) and (-18, 8) respectively:
(a)What is the equation (in slope-intercept form) of the line determined by these two points?
(b)What is the gradient of the line perpendicular to this line?
(c) What is the distance between points A and B?
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! HI there,
a) Gradient = y2 - y1/x2 - x1
Using (6,-4) and (-18,8)
Gradient = 8 - (-4)/-18 - 6
Gradient = 8 + 4/-24
Gradient = 12/-24 = -1/2
Using equation of the line
y - b = m(x - a) and (6, -4)
y -(-4) = -1/2 (x - 6)
y + 4 = -1/2x + 3
y = -1/2x + 3 - 4
y = -1/2x - 1
or
2y = -x - 1
.........
b)A line that is perpendicular to
another line have gradients that
multiply together to give -1
m1 x m2 = -1
-1/2 x m2 = -1
m2 = 2
Gradient of line perpendicular
to the first line has a gradient = 2
...........
c) Distance formula
Sqrt (x2 - x1)^2 + (y2 - y1)^2
A (6, -14) B (-18, 8)
sqrt (-18 - 6)^2 + (8 - (-14)^2
sqrt(-24)^2 + (22)^2
sqrt 1060
= 32.6 units
Hope this helps:-)
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