Math, asked by xyz6624, 1 year ago

the vertices of a triangle ABC are A( - 3 , 2) B (- 1 ,- 4 ) and C (5 , 2) to if m and n are the midpoints of AB and AC respectively show that 2 MN is equals to BC​

Answers

Answered by AditiHegde
2

The vertices of a triangle ABC are A( - 3 , 2) B (- 1 ,- 4 ) and C (5 , 2) to it m and n are the midpoints of AB and AC respectively.

Given,

A( - 3 , 2) B (- 1 ,- 4 ) and C (5 , 2)

M is the mid-point of AB

N is the mid-point of AC

Mid-point formula is given by,

(x, y) = { (x1 + x2) / 2 , (y1 + y2) / 2 }

The mid-point of AB is

M (x, y) = { ( -3 -1 ) / 2 , ( 2 - 4 ) / 2 } = ( -2, -1)

M( -2, -1)

The mid-point of AC is

N (x, y) = { ( -3 + 5 ) / 2 , ( 2 + 2 ) / 2 } = ( 1, 2)

N( 1, 2)

Distance formula is given by,

d = √ [ (x2 - x1)^2 + (y2 - y1)^2 ]

The distance between B and C

BC = √ [ (5 +1)^2 + (5 +4)^2 ]

= √ [ 6^2 + 9^2 ]

∴ BC = √ (117)

The distance between M and N

MN = √ [ (1 +2)^2 + (2 +1)^2 ]

= √ [ 3^2 + 3^2 ]

∴ MN = √ (18)

∴ 2 MN = BC

Hence it is shown that 2 MN = BC

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