Question

find the length of the median through the vertex b of a triangle abc with vertices A(9,-2),B(-3,7) and C(-1,10)

Answer 1

Given:

A triangle ABC with vertices A(9,-2),B(-3,7) and C(-1,10)

To find:

The length of the median through vertex B.

Solution:

We know that the median of any of the triangle is the mid-point of the sides of the triangle so,

D is the mid-point of the AC

Let the coordinate of point D is (x,y)

Point D is given by:

• $(x,y) = \frac{x1+x2}{2} , \frac{y1+y2}{2}$
• $(x,y) = \frac{9-1}{2} , \frac{-2+10}{2}$
• $(x,y) = \frac{8}{2} , \frac{8}{2}$
• $(x,y) = (4,4)$

Now we will find the length of the median BD by the distance formula,

• $\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$
• $\sqrt{(9-4)^{2}+(-2-4)^{2}}$
• $\sqrt{(5)^{2}+(-6)^{2}}$
• $\sqrt{25+36}$
• $\sqrt{61}$

The length of the median through vertex B is $\sqrt{61}$ units

Answer 2

Answer:

the answer is right up

Step-by-step explanation:

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