Question

What are the coordinates of the point that is 1/6 of the way from a(14,-1) b(-4,23)

Answer 1

Answer:

$\text{The coordinates of point is }P(a,b)=(\frac{80}{7}, \frac{17}{7})$

Step-by-step explanation:

$\text{Given the coordinates of point that is }\frac{1}{6}\text{ of the way from a(14, -1), b(-4, 23)}$

$\text{If a point }P(a, b)\text{ divides the line joining two points }(x_1,y_1)\text{ and }(x_2, y_2)\\ \text{ in the ratio m:n internally, then the coordinates of point P are given by}$

$P(a,b)=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})$

The two points given are a(14, -1), b(-4, 23) and ratio m:n=1:6

$P(a,b)=(\frac{1(-4)+6(14)}{1+6}, \frac{1(23)+6(-1)}{1+6})$

$P(a,b)=(\frac{80}{7}, \frac{17}{7})$