Please anyone that knows math help me?

Question

Calculate the slope between the points (3, 7) and (-3, 7).

If line MN is the diameter of a circle with M(-3, -4) and N(-7, -14), find the center of the circle

What is the y-intercept of 12x + 4y = 10

. Where P is (-2, 6), R is (-10, 4), and segment RT is a diameter of center point P, find the coordinates of T.

Answer 1

1. The slope is a measure of how the line rises or falls.

If you have two points, the slope is calculated by: (difference of y-coordinates) / (difference of x-coordinates).

Your question: (y2 - y1)/(x2 - x1)
= (7 - 7)/(-3 - 3) = 0/-6 = 0

The y-coordinates are the same, therefore this is a horizontal line, with slope = 0.


2. If you have the end-points of a diameter, then the centre of the circle is the centre of the diameter-line.

For a line with endpoints (x1, y1) and (x2, y2), the midpoint has coordinates ( (x1 + x2)/2, (y1 + y2)/2 )

That is, half-way between the x's and half-way between the y's.

Therefore, the centre is ( (-3+7)/2, (-4+14)/2 ) = (2,5)


3. If the equation of a line is put into standard form: y = mx + b,
then 'b' is the y-intercept.

You can see that if you set x=0, then y=b. By definition, the y-intercept occurs when x=0.

Rearranging your equation:
12x + 4y = 10
4y = -12x + 10
y = -3x + 10/4

Therefore the y-intercept is at 2.5 (10/4).


4. This can be done by extension of question 2. Now we are given the centre and one point on the circle itself, and we have to calculate the coordinates of the point that is the other end of the diameter.

Let the other point T be (x2, y2).
Let the coordinates of P be (xc, yc) (the centre) and the coordinates of R be (x1, y1)

Then xc = (x1 + x2) / 2
2xc = x1 + x2
x2 = 2xc - x1
= 2(-2) - (-10)
= -4 + 10
= 6

Similarly y2 = 2yc - y1
= 2(6) - 4
= 12-4
= 8

Therefore the coordinates of T are (6,8)

Answer 2

The slope is zero

The center is at (-5, -9)

The y-intercept is at 2.5

T is at (6, 8)

HTH

Doug