On a number line, the directed line segment from q to s has endpoints q at –8 and s at 12. point r partitions the directed line segment from q to s in a 4: 1 ratio. which expression correctly uses the formula to find the location of point r?

The expression that shows the location of R is,

Step-by-step explanation:

Since, the x-coordinate of a point on the number line shows its location.

Here, the location Q and S are -8 and 12 respectively.

⇒ x-coordinates of point Q and point S are -8 and 12 respectively.

Q and S are lying on the number line,

⇒ Coordinates of Q and S are  (-8,0) and (12,0) respectively.

Now, If a point divides a line segment having end points and in the ratio m:n

Then by the section formula,

The coordinates of the point are,

Here, point R partitions the directed line segment from Q to S in a 4:1 ratio.

Thus, by the above formula, the coordinates of R

=

=  

x-coordinate of R  =  

⇒ Location of R =  

Which is the required expression.

1/5^2 = 7.56/45