Question

A triangle has certified C (1,4), D (-2,2) and E (3,1).

Answer 1

Answer:

The equation for the median from vertex C is

$y=5x-1$

Step-by-step explanation:

we know that

The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side

In this problem

Is a line segment joining vertex C to the midpoint segment DE

step 1

Find the midpoint segment DE

we have

D (-2,2) and E (3,1)

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the given values

$M(\frac{-2+3}{2},\frac{2+1}{2})$

$M (0.5,1.5)$

step 2

Determine equation of the median

The median passes through the points

C(1,4) and M(0.5,1.5)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{1.5-4}{0.5-1}$

$m=\frac{-2.5}{-0.5}$

$m=5$

Find the equation in point slope form

$y-y1=m(x-x1)$

we have

$m=5\\C(1,4)$

substitute

$y-4=5(x-1)$

Convert to slope intercept form

Isolate the variable y

$y-4=5x-5\\y=5x-5+4\\y=5x-1$

therefore

The equation for the median from vertex C is

$y=5x-1$