Question

the point n lies on the segment mp. find the coordinates of n so that mn is 7/9 of mp. m (-22, 32) p (5, -4) coordinates of n: (?,?)

Explanation:

Step1: Use section - formula

If a point $N(x,y)$ divides the line - segment joining $M(x_1,y_1)$ and $P(x_2,y_2)$ in the ratio $m:n$, the coordinates of $N$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $M(-22,32)$, $P(5,-4)$, and the ratio $m:n = 7:2$ (since $MN=\frac{7}{9}MP$, so the ratio of $MN$ to $NP$ is $7:2$).

Step2: Calculate the $x$ - coordinate of $N$

$x=\frac{7\times5+2\times(-22)}{7 + 2}=\frac{35-44}{9}=\frac{-9}{9}=-1$.

Step3: Calculate the $y$ - coordinate of $N$

$y=\frac{7\times(-4)+2\times32}{7 + 2}=\frac{-28 + 64}{9}=\frac{36}{9}=4$.

Answer:

$(-1,4)$