Question

AB is a directed segment with endpoints A(2,2) and B(14,14). In two or more complete sentences, explain how you would verify that Point X, with a coordinate of (6,6), divides AB in a 1:2 ratio?

Answer 1

The smaller side is 4 units going from point (2,2) to point (6,6) while the biger side is 8 units long going from point (6,6) to point (14,14). So 4 is 1/2 of 8 therefore there is a 1:2 ratio because of 4:8

Answer 2

Answer:

Yes, point X, with a coordinate of (6,6), divides AB in a 1:2 ratio

Step-by-step explanation:

We have been given the endpoints for AB as A(2,2) and B(14,14). The point X divided the line segment AB in 1:2 ratio and the coordinate of X is (6,6)

We know that if a point divides a line segment in m:n ratio then the coordinate of the point is given by

$\left ( \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n} \right )$

On substituting the known values, we can find the coordinate of X and check if it is same with the given coordinate or not

$X=\left ( \frac{1\cdot 14+2\cdot 2}{2+1},\frac{1\cdot 14+2\cdot 2}{2+1} \right )\\\\X=\left ( \frac{18}{3},\frac{18}{3}\right )\\\\X=(6,6)$

Since, we got the same X coordinate as the given.

Hence, the given statement is verified.