Math GEniuses!! pls help me!!!!?

Question

M (1,-5) is the midpoint of RS (with a horizontal line above it). If S has coordinates (5,1), find the coordinates of R.

pls explain thoroughly. THANKS!!!

Answer 1

A midpoint happens exactly halfway between two points.

Your first point is R, so just call that (x,y). The second point is at (5,1). The midpoint has coordinates that are the average of the these two points.

The x-coordinate of M = 1, which should be the average of x and 5. You write this as:
(x + 5) / 2 = 1

Solve for x to get:
x + 5 = 2
x = -3

Do the same for the y-coordinate:
(y + 1) / 2 = -5
y + 1 = -10
y = -11

So the answer is:
R is (-3, -11)

Answer 2

the midpoint formula goes as follows...

([X1+X2]/2), ([Y1+Y2]/2)

the x's and y's are the endpoints of the segment, the (blah), (blah) from the coordinates of the midpoint. so we can plug in numbers

we know the X value of the midpoint to be 1.

(5+X)/2=1
X+5=2
X= -3

The X value of the answer is -3

Now for the Y value

(1+Y)/2= -5
Y+1= -10
Y= -11

Soooo the coordinates of R are (-3, -11)

Answer 3

M is midpoint of line RS, both co-ordinates are given (M and S), so the SLOPE from point M to S is the same slope for M to R.

SLOPE = ((y2-y1)/(x2-x1)) = [(-1-(-5)) / (5-1) ] = 4/4

4/4 = (up 4, right 4) or (down 4, left 4)

starting from point M (1,-5) go down 4 then left 4....

(1 - 4),(-5-4) = R ( -3, -9 )

Answer 4

Easy. To get from M to S you add 4 to the x coordinate and 6 to the y coordinate. To get from M to R you SUBTRACT 4 from the x coordinate and SUBTRACT 6 from the y coordinate.

R=(-3,-11)

Answer 5

remedy for y 4x - 2y = -8 4x - 2y +2y= -8 +2y (upload 2y to the two facets) 4x = -8 + 2y 4x + 8 = -8 +2y + 8 (upload 8 to the two facets) 4x +8 = 2y 2x + 4 = y it is in 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 easy. purely set y=0 so which you get 4x -2(0) = -8 4x = -8 x = -2

Answer 6

mid point = {(x1+x2)/2,(y1+y2)/2)}

so 1=(5+x)/2
and -5=(1+y)/2