Question

Find the length of the median drawn through A on BC of a ∆ABC, whose vertices are A(7, −3), B(5, 3) and C(3, −1)

Answer 1

Answer:

5 units

Step-by-step explanation:

Given A(7, -3), B(5, 3) and C(3, -1) be the vertices of triangle ABC.

Midpoint of line segment joining 2 points (x₁, y₁) and (x₂, y₂) is given by

(x₁ + x₂/2, y₁ + y₂/2)

Now, midpoint of BC is D(4, 1).

Median through A is the line joining A and the midpoint of BC i.e.,D

=> Length of the median is the distance between the 2 points A and D,

Distance between 2 points (x₁, y₁) and (x₂, y₂) is given by

√(x₁-x₂)² + (y₁-y₂)²

Distance between the points A and D is

√(7-4)² + (-3-1)²

=√3² + 4²

=5 units

Answer 2

Answer:

5 UNITS

Step-by-step explanation:

WE KNOW THAT MEDIAN DIVIDES ANY SIDE IN TWO EQUAL PARTS

SO, LET US DRAW A TRIANGLE ABC AS SHOWN IN FIGURE BELOW AND LET US MAKE MEDIAN D ON SIDE BC.

THEN D WILL BE THE POINT THAT WILL DIVIDE THE LINE BC INTO TWO EQUAL HALVES

THUS, WE'LL US MIDPOINT FORMULA FOR FINDING D BECAUSE WE KNOW THE COORDINATES OF B&C

MIDPOINT FORMULA IS (X1 + X2)/2 , (Y1+Y2)/2 FROM THIS WE'LL GET COORDINATES OF D

D WILL BE 4,1

THEN WE'LL FIND AD BY DISTANCE FORMULA

DISTANCE WILL BE 5 UNITE

HOPE U WILL FIND THE ANSWER (^_^)