Math Snap

STEP 1

Assumptions1. The endpoints of the line segment $\overline{AB}$ are given.
. We need to find the coordinates of the point $$ that partitions the segment in the given ratio.
Let's start with problem15.

STEP 2

The formula to find the coordinate of a point that divides a line segment in a given ratio is$$= \frac{mB + nA}{m + n}$$where $A$ and $B$ are the coordinates of the endpoints, and $m:n$ is the given ratio.

STEP 3

For problem15, the endpoints are6 and16, and the ratio is1. Plug these values into the formula.
$$= \frac{ \cdot16 +1 \cdot6}{ +1}$$

STEP 4

Perform the multiplication in the numerator.
$$= \frac{64 +6}{}$$

STEP 5

Add the values in the numerator.
$$= \frac{70}{5}$$

STEP 6

Divide the numerator by the denominator to find the coordinate of point $$.
$$=70 /5 =14$$For problem15, the coordinate of point $$ is14.
Now, let's solve problem16.

STEP 7

For problem16, the endpoints are -9 and6, and the ratio is14. Plug these values into the formula.
$$= \frac{1 \cdot6 +4 \cdot -9}{1 +4}$$

STEP 8

Perform the multiplication in the numerator.
$$= \frac{6 -36}{5}$$

STEP 9

Subtract the values in the numerator.
$$= \frac{-30}{5}$$

Divide the numerator by the denominator to find the coordinate of point $$.
$$= -30 /5 = -6$$For problem16, the coordinate of point $$ is -6.