Triangle $abc$ has vertices at $a(5,8)$, $b(3,-2)$, and $c(6,1)$. the point $d$ with coordinates $(m, n)$ is chosen inside the triangle so that the three small triangles $abd$, $acd$ and $bcd$ all have equal areas. what is the value of $10m + n$?

10m + n = 49

Explanation:

Point D will be the centroid of ABC. To find the centroid we use formula.

Given the coordinates of the three vertices of a triangle ABC,

the centroid D coordinates are given by -

m = (x₁ + x₂ + x₃)/3      &      n = (y₁ + y₂ + y₃)/3

m =

m =

and

n =

n =

Now we will find the value of 10m+n

=

=

= 49

So, 10m + n = 49

That's the final answer.

step-by-step explanation:

ok so im not 100% sure but you would start by adding 5.1t and 1.9t beacuse they have the same variable. that is 7t.   then add -3.6 + 1.2 which is -2.4

so then keep that as -2.4 + 7t. i apologize if this is incorrect. best luck on your test < 3

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step-by-step explanation: