math geniuses!! pls help me!!!?

Question

M(-6, -2) is the midpoint of RS (with a line above it). If S has cooridnates (1,2), Find the cooridinates of R.

PLEASE explain step by step. THANKS!!

Answer 1

R is the point (- 13, - 6).

This was both FOUND, and CHECKED, as follows:

If M (-6, -2) is the midpoint of the line RS, and S has coordinates (1, 2), R has to be on the other side of M by exactly the same amount that M is away from S.

Relative to S, M is at (-7, -4), since its x-coordinate is S's (1) - 7 = -6; and its y-coordinate is S's (2) - 4 = - 2. So R must have coordinates as follows: -6 (M's x-coordinate) -7 = - 13; and -2 (M's y-coordinate) - 4 = - 6.

So R is the point: (- 13, - 6). ***

CHECK (It's always good to do a check!): IF M is the mid-point of the line RS, its coordinates must in fact be exactly half the sum of the separate x- and y-coordinates of R and S. O.K. let's now check that this is true for the values we found:

x-coordinates: (- 13 + 1)/2 = - 6 (M's x-cooordinate: Good.)
y-coordinates: (- 6 + 2)/2 = -2 (M's y-cooordinate: GREAT!)

So we have confirmed that M is indeed the midpoint of the line RS that we have constructed, and therefore that:

R is indeed the point (- 13, - 6).

Live long and prosper.

*** Later addition: Notice that the SOLUTION, found in this PURELY ARITHMETIC WAY, is a fair bit shorter than the next three algebraic solutions. That will often be the case. What's more, I was able to use the "midpoint calculation" --- for the midpoint of the line RS --- as a CHECK. So far, no other responder has provided a CHECK on the correctness of his/her conclusion.

It is always sound practice to provide such a check. Otherwise, one is left simply having to trust that no mistakes have been made in the algebra. In light of the general quality of algebra in Yahoo! Answers, I leave it to you to judge for yourself whether that is wise.

Answer 2

Midpoint is

((x1 + x2) / 2 , (y1 +y1)/2)

Take S as point 1

Now look at x separately,

-6 = (1 + x2)/2

Multiply by 2

-12 = 1 + x2

Subtract 1 from both sides

-13 = x2


----

Do the same for y

-2 = (2 + y2)/2

Mutiply both sides by 2

-4 = 2 + y2

Subtract 2 from both sides

-6 = y2

-----

So R = (-13,-6)

Best of luck!

Answer 3

Let ( x1 , y1 ) be the Co-ordinates of R and ( x2 , y2 ) be the Co-ordinates of S

M ( -6 , -2) and S ( 1, 2) and R (x1 , y1)

Mid - Points Of RS is M

M = { ( x1 + x2 ) / 2 ; ( y1 + y2 ) / 2 }

- 6 = ( x1 + 1 ) / 2 ; - 2 = ( y1+ 2 ) / 2

x1 + 1 = - 12 ; y1 + 2 = - 4

x1 = - 12 - 1 ; y1 = - 4 - 2

x1 = - 13 ; y1 = - 6

Therefore, The Co-ordinates of R is ( - 13 , - 6)

Answer 4

the formula for the middle is:

(( x1 + x2 )/2, ( y1 + y2) /2 )

so lets take S as (x1 , y1):


( 1 +x2 ) / 2 = -6 and (2 + y2 ) /2 = -2
meaning 1 +x2 = -12 and 2 +y2 = -4
x2 = -13 and y2 = -6

so R (-13,-6)

Answer 5

sparkling up for y 4x - 2y = -8 4x - 2y +2y= -8 +2y (upload 2y to the two components) 4x = -8 + 2y 4x + 8 = -8 +2y + 8 (upload 8 to the two components) 4x +8 = 2y 2x + 4 = y it is interior the kind mx + b the place m is the slope and b is the y-intercept. for this reason slope = 2 y intercept = 4 Calculating x-intercept is trouble-free. in simple terms set y=0 so which you get 4x -2(0) = -8 4x = -8 x = -2

Answer 6

-6=(1+x)/2
-12=1+x
x=-13

-2=(y+2)/2
-4=y+2
y=-6

R(-13, -6)