Question

Q1.The vertices of a Δ ABC are A(-3,3), B(-1,-4) and C(5,-2).M and N are the mid points of AB and AC. Show that MN=1/ 2 BC.

Answer 1

Answer:

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Step-by-step explanation:

Given: A(−3,2),B(−1,−4) and C(5,2) and M is the midpoint of AB and N is the midpoint of AC.

Using the formula of midpoint:

x=

2

x

1

+x

2

;y=

2

y

1

+y

2

For Point M: x=

2

−3−1

=−2;y=

2

2−4

=−1=(−2,−1)

For Point N:x=

2

−3+5

=1;y=

2

2+2

=2=(1,2)

Using distance Formula:

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

Distance between M and N=

(1+2)

2

+(2+1)

2

MN=

3

2

+3

2

=

9+9

=

18

=3

2

Distance between B and C=

(5+1)

2

+(2+4)

2

MN=

6

2

+6

2

=

36+36

=

72

=6

2

Therefore, BC=2MN