Question

In a triangle ABC,if A=(3,2), B=(1,4), and the mid point of AC is (2,5), then the mid point of BC is​

Answer 1

Step-by-step explanation:

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Answer 2

The midpoint of BC is (1,6) .

Explanation:

• The midpoint of a line joining points (a,b) and (c,d) =$(\dfrac{a+b}{2},\dfrac{c+d}{2})$

Given : In a triangle ABC,if A=(3,2), B=(1,4), and the mid point of AC is (2,5).

Let the coordinates of point C=(x,y).

Then , the midpoint of AC will be

$(\dfrac{3+x}{2},\dfrac{2+y}{2})=(2,5)\\\\ \dfrac{3+x}{2}=2\ \ ,\ \ \dfrac{2+y}{2}=5\\\\ 3+x=2(2),\ ,\ 2+y=2(5)\\\\ 3+x=4,\ ,\ 2+y=10\\\\ x=1 ,\ y=8$

∴ coordinates of point C=(1,8)

Then , the midpoint of BC will be

$(\dfrac{1+1}{2},\dfrac{4+8}{2})=(1,6)$

Hence, the midpoint of BC = (1,6)

#Learn more :Point c is called a mid point of a line segment AB. prove that every line segment has one and only one mid point

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