If you have one coordinate and a midpoint, how do you find the other coordinate?

Question

For a line segment AB, one endpoint is A(0,6) and the midpoint is M(4,7) find the coordinates of endpoint B.

yes thats the answer....but HOW?

thanks people you guys are the best...got the answer! :P

Answer 1

The midpoint is between the two endpoints, so the midpoint is the average of the endpoints.
([x1]+[x2])/2=Midpoint x
([y1]+[y2])/2=Midpoint y
([0]+[x2])/2=4
([6]+[y2])/2=7

(8,8)

Answer 2

Usually, when you have a midpoint and a point the solution will require the use of the distance formula and slope formula. First you can set the slope equation of A to M equal to M to B: (7-6)/(4-0)=(7-y)/(4-x); simplified that means x-4y=-24. Then you can find the distance between A and M: D^2=(0-4)^2+(6-7)^2; simplified as the square root of 17. Since you know the distance between M and B should be the same you can set the square root of 17 equal to the distance equation between B and M: (17^(1/2))^2= (4-x)^2+(7-y)^2; simplified as x^2-8x+y^2-14y=-48. Then you solve the system; first solve for x or y in the slope equation, simplifying as x=4y-24. You can substitute this x-value into the distance equation to solve for y. You get 0=17(y-8)(y-6); or y=8 and y=6. The values could then be substituted into the x-4y=-24 equation in order to get the x-values. The results are (0,6), or A, and (8,8), now B. Therefore your final answer is B(8,8).

Answer 3

The answer is B(8,8),
when A(0,6) and M(4,7), then vector AM would be "coord.M" -"coord.A" , that is: AM=(4-0,7-6) => AM=(4,1)
this means that from A to M there is a distance of 4 units in the x direction, and 1 unit in the y direction,
so to find B which is on the extended AM line with doubled length, you sould double the components of AM, AB=2AM (both vectors) => AB=(8,2),
so we now know the vector pointing from A to B, if we want to find the coord for B, then we use the same rule applied at first which is : OB-OA=AB , OB is the vector pointing from origin to B which has the values of B coordinates as components. so, B=OB=AB+OA=(8,2)+(0,6)=(8,8)

Answer 4

Find the slope from A to M using the equation y2-y1/x2-x1.
y2-y1/x2-x1
7-6/4-0
1/4 = slope
Next, add this slope to M but remember to put y/x instead of x/y.
7/4+1/4
8/8
Finally, switch the x and y again to get your B coordinates
B(8, 8)

Answer 5

Since M is the midpoint between A and B,

B = M + (M - A)

B= 2M - A

XB = 2XM - XA
YB = 2YM - YA