Question

If the points (2,7),(-3,3) and (5,1) are the vertices of a triangle ,find the length of the median drawn through the first vertex.​

Answer 1

Answer:

• $\sqrt{26}$ units

Step-by-step explanation:

The median is the line segment connecting the vertex with the midpoint of the opposite side.

The midpoint has coordinates:

• x = (-3 + 5)/2 = 2/2 = 1
• y = (3 + 1)/2 = 4/2 = 2

Use the distance formula to find the distance between points (2, 7) and (1, 2):

• $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
• $d=\sqrt{(1- 2)^2+(2-7)^2} =\sqrt{1+25} =\sqrt{26}$

Answer 2

Step-by-step explanation:

the formula for the length of a median based on the 3 side lengths is

m = sqrt(2AB² + 2AC² - BC²)/2

where BC is the side opposite of the indicated vertex.

let's say

A = (2, 7)

B = (-3, 3)

C = (5, 1)

AB² = (2 - -3)² + (7 - 3)² = 5² + 4² = 25 + 16 = 41

AC² = (2 - 5)² + (7 - 1)² = (-3)² + 6² = 9 + 36 = 45

BC² = (-3 - 5)² + (3 - 1)² = (-8)² + 2² = 64 + 4 = 68

m = sqrt(2×41 + 2×45 - 68)/2 = sqrt(82+90-68)/2 =

= sqrt(104)/2 = sqrt(104/4) = sqrt(26) =

= 5.099019514...