Question

The midpoint of AB is M(6,2). If the coordinates of A are (4,8), what are
the coordinates of B?

Answer 1

B = (8,-4)

The midpoint formula is (xm,ym) = ((x1+x2)/2, (y1+y2)/2).
(6,2) = ((4+8)/2, (8+(-4))/2)

Answer 2

Explaination :

★ Given that,

• The midpoint of AB is M(6 , 2)
• The coordinates of A are (4 , 8)

★ To calculate,

• Coordinates of point B?

So here we would be using the formula of calculating the midpoint of two points.

Midpoint of two points:-

• $\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar$

★ We have :

• x1 = 4
• y1 = 8

★ Putting the values :

• Refer to the attachment.

★ Therefore,

• Coordinates of the point B is (8 , -4)

Additional Information :

★ Centroid of a triangle :-

• $\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} }} \: \pink\bigstar$

★ Distance Formula :-

• $\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar$