Question

In the given figure BMCDE is a straight line where D and C are mid points of CE and BE respectively. Find the length (in units) of triangle ABC's median AM if E (6,5), D (3,5) and A (4,8). ​

Answer 1

Step-by-step explanation:

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Answer 2

The length of the Median AM of triangle ABC is $\sqrt{58}$ units.

Given:

BMCDE is a straight line.

D is the mid-point of CE and C is the mid-point of BE.

E(6,5)

D(3,5)

A(4,8)

AM is the median of Triangle ABC.

To Find:

Length of Median AM.

Solution:

As D is the mid point of CE, and C is the mid point of BE.

CD = DE, and

BC = CE

Hence, the coordinates of C is (0,5).

Also as AM is the median of triangle ABC,

BM = MC

Hence, the coordinates of M and B are (-3,5) and (-6,5) respectively.

We need to find the length of median AM,

using the distance formula,

$d=\sqrt{(x_2 - x_1)^2 +(y_2-y_1)^2}$

The distance between A(4,8) and M(-3,5) is,

$d=\sqrt{(4-(-3)^2+(8-5)^2}\\ d=\sqrt{(4+3)^2+3^2}\\ d=\sqrt{7^2+9}\\ d=\sqrt{49+9}\\ d=\sqrt{58}$

Hence, the length of the Median AM of triangle ABC is $\sqrt{58}$ units.

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