Question

The line segment, AB has a point C as its midpoint. If A is at (2,2) and C is at (5,4) what are the coordinates of the endpoint B
A:(-1,0)
B:(3.5,3)
C:(5,4)
D:(8,6)

Answer 1

Answer:

( 8 , 6 )

Step-by-step explanation:

A = ( 2 , 2 ) and C = ( 5 , 4 )

→ Form an equation

$\frac{2+x}{2} =5$   and   $\frac{2+y}{2}=4$

→ Now solve them

2 + x = 10 and 2 + y = 6

→ Simply find the values

x = 8 and y = 6

Answer 2

• Let the coordinates of B be ( x , y ). Now , Let A ( 2 , 2 ) be ( x₁ , y₁ ) & B ( x , y ) be ( x₂ , y₂ )

SOLUTION :

• All you need to apply is the formula of Midpoint i.e $\sf{ \bold{( \frac{x_{1} + x_{2}}{2} \: , \frac{y_{1} + y_{2}}{2} )}}$

• Plug the known values :

$\large{ \rightarrow{ \tt{ \: (5 \: ,4 \: ) = ( \frac{2 + x}{2} \: , \frac{2 + y}{2} )}}}$

• Equating corresponding values :

$\large{ \tt{5 = \frac{2 + x}{2} }}$

$\large{ \rightarrow{ \tt{10 = 2 + x}}}$

$\large{ \rightarrow{\tt{10 - 2 = x}}}$

$\boxed{ \large{ \rightarrow \tt{x = 8}}}$

• Value of x = 8

$\large{ { \tt{4 = \frac{2 + y}{2} }}}$

$\large{ \rightarrow{ \tt{8 = 2 + y}}}$

$\large{ \rightarrow{ \tt{8 - 2 = y}}}$

$\boxed{ \large{ \rightarrow{ \tt{y = 6}}}}$

• Value of y = 6

$\large{ \boxed{ \tt{OUR \: FINAL \: ANSWER : \: D. \: (8 \:, 6 \: ) }}}$

:) Hope I helped! Let me know if you have any questions regarding my answer! ~