Question

the point n lies on the segment mp. find the coordinates of n so that the ratio of mn to mp is 4 to 5. m(-6,5) n(?,?) p(21,-13)

Explanation:

Step1: Recall section - formula

The coordinates of a point $N(x,y)$ that divides the line - segment joining $M(x_1,y_1)$ and $P(x_2,y_2)$ in the ratio $m:n$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-6,y_1 = 5,x_2 = 21,y_2=-13,m = 4,n = 1$.

Step2: Calculate the x - coordinate of N

$x=\frac{4\times21+1\times(-6)}{4 + 1}=\frac{84-6}{5}=\frac{78}{5}=15.6$.

Step3: Calculate the y - coordinate of N

$y=\frac{4\times(-13)+1\times5}{4 + 1}=\frac{-52 + 5}{5}=\frac{-47}{5}=-9.4$.

Answer:

$(15.6,-9.4)$