Question

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 $10m + n$?

Answer 1

Answer:

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 = $\frac{5 + 3 + 6}{3}$

m = $\frac{14}{3}$

and

n = $\frac{8-2+1}{3}$

n = $\frac{7}{3}$

Now we will find the value of 10m+n

= $10*\frac{14}{3} + \frac{7}{3}$

= $\frac{140}{3} + \frac{7}{3}$

$= \frac{147}{3}$

= 49

So, 10m + n = 49

That's the final answer.