geometry help?

Question

a triangle has vertices A(1,1) B(2,4) C(4,2)
Write a equation for a line parallel to AB and contains point C

Answer 1

first we need to find the slope of the AB it is
(4-1)/(2-1)=3

we need only slope and a point to draw a line so

y-2=3(x-4) so
the answer is
y=3x-10

Answer 2

okay the fisrt thing to do is learn this formula it tells us the gradient of a line from a set of cordinates.

The formula is (y1-y2) divided by (x2-x1)

In this case y2 is 4, y1 is 1 and x2 is 2, x1 is 1. So y2 - y1 = 3

and x2 -x1 is 1 so 3/1 is 3. The gradient of the line AB is 3 and becuase parrelle lines have the exact same gradient the gradient of the parallel line also is 3.

So far the equation of the parrellel line is y=3x + c

C is the y intercept, to work out C we insert the values of cordinate c (4,2)

So 2=3(4) +c

2=12 +c
2- 12= c
-10 =c

So finally the equation of the line is Y=3x-10

Answer 3

First find the slope of line AB: (4-1)/(2-1)=3.
Next use the point slope formula to make a line with this slope passing through point C: y-2=3(x-4)
y-2=3x-12 or y=3x-10.

Answer 4

The equation is y = 3x - 10

The slope of line AB is 3, so a parallel line is also slope of 3.

The y-intercept is -10, therefore the equations is correct above. Plug in the values for C (4,2) to check my work.

Answer 5

find the slope of AB

(y2 - y1) / (x2 - x1)

(4 - 1) / (2 - 1)
3 / 1
slope = 3

the new equation will have the same slope since the two lines are parallel so lets substitute the slope into the equation:

y = mx + b

m = slope
b = y-intercept

y = 3x + b

so we have to find the y-intercept...plug the coordinates of C into the new equation and solve for "b":

2 = 3(4) + b
2 = 12 + b
b = -10

plug "b" into our new equation and the answer is:

y = 3x - 10

Answer 6

y= 3x -10

AB your slope is 3 (hence 3x). going through c (2,4) that line also going down 3 for every 1 left, will pass through -10 at the axis.... hence your (-10)

hope this helps ;-)