Thread: Slope...

Can you guys show me how to do these problms?? I was sick yesterday and today and wasnt able to go to my Math class...

1.Find the eqn of the line passing thru the midpoint of the line segment joining A(-3,2)) and (1,6) with slope half the slope of the line passsing A and B

2.Find the eqn of the line perp. to line -2x-y=-10 and having the midpot. of the segment of the line 2x+y=4 from its x-int. to its. y-int.

3.Pts. A(-8,-16) B(0,10) and C(12,14) are three vertices of a parralelogram. Find the coordinates of the 4th Vertex if its located in the 3rd Quadrant

4.Givenn the line 2x-3y=2, rewrte:
a. in point slope fom
b. in slope-int. form
c. in 2pt. form

Thank you guys!!!

Originally Posted by AndrewK

1.Find the eqn of the line passing thru the midpoint of the line segment joining A(-3,2)) and (1,6) with slope half the slope of the line passsing A and B

I presume point B is (1, 6)?

The midpoint of the line segment between points A and B is:
((-3 + 1)/2, (2 + 6)/2) = (-1, 4)

The slope of the line segement between points A and B is:
(2 - 6)/(-3 - 1) = -4/-4 = 1

So half of this slope is 1/2. We need the equation for the line that has a slope of 1/2 and passes through the point (-1, 4).

y = (1/2)x + b
where b is the y-intercept.

To find b, just plug in a point on the line. The only point we know is (-1, 4), so...
4 = (1/2)*(-1) + b

4 = -1/2 + b

b = 4 + 1/2 = 9/2

Thus the line is:
y = (1/2)x + (9/2)

-Dan

Originally Posted by AndrewK

2.Find the eqn of the line perp. to line -2x-y=-10 and having the midpot. of the segment of the line 2x+y=4 from its x-int. to its. y-int.

Let's find that midpoint first.
2x + y = 4

y = -2x + 4

The y-intercept is the point (0, 4), which you can read off from the equation, or just plug in the x value of 0 and find out what y is.

To find the x-intercept put y = 0 and solve for x:
0 = -2x + 4

-2x = -4

x = -4/-2 = 2

So the x-intercept is the point (2, 0). We need the midpoint of the line segement going from (2, 0) to (0, 4):
((2 + 0)/2, (0 + 4)/2) = (1, 2)

Now we need to know the slope of the line we want. This is perpendicular to the line -2x-y=-10. Putting this into slope-intercept form:
-y = 2x - 10

y = (-2)x + 10

The slope of this line is -2. Thus the slope of the line perpendicular to it is -1/(-2) = 1/2.

So we need a line with a slope of 1/2 going through the point (1, 2). This is done in exactly the same way I showed you in the first problem. I'll give you the solution:
y = (1/2)x + (3/2)

If you have a problem finding this, just let me know.

-Dan