Question

Find the coordinates of one endpoint of a segment if one endpoint is (6, 3) and the midpoint is (1, 5).

A.
(2, 4)

B.
(– 4, 7)

C.
(2.5, 4)

D.
(4, 7)

Answer 1

Answer :

• Coordiantes of another end point would be (-4, 7)

Option B : (-4,7) is correct.

Given :

• For a line segment one endpoint is given as (6,3) and the midpoint of segment is (1,5)

To find :

• Second endpoint of the line segment , ( x,y ) = ?

Formula required :

• Midpoint formula

$\red{\bigstar}\boxed{\sf{(x\;,\;y)=\left(\dfrac{x_1+x_2}{2}\;,\;\dfrac{y_1+y_2}{2}\right)}}$

[ Where (x,y) are coordinates of point giving the mid point of a line segment joining points (x₁,y₁) and (x₂,y₂) ]

Solution :

Using Mid point formula

$\implies\sf{(1\;,\;5)=\left(\dfrac{(6+x)}{2} \;,\;\dfrac{(3+y)}{2}\right)}$

so,

$\implies\sf{1=\dfrac{6+x}{2}\;\;\;,\;\;\;5=\dfrac{3+y}{2}}$

$\implies\sf{6+x=2\;\;\;,\;\;\;3+y=10}$

$\implies\sf{x=2-6\;\;\;,\;\;\;y=10-3}$

$\implies\underline{\boxed{\red{\sf{x=-4\;\;\;,\;\;\;y=7}}}}$

Therefore,

• Coordinates of another end point are (-4, 7).