Question

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?

Answer 1

Explanation:

Answer: The expression that shows the location of R is,

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.

Answer 2

Answer: The expression that shows the location of R is,

`(4* 12+ 1* -8)/(4+1)`

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
`(x_1,y_1)` and
`(x_2,y_2)` in the ratio m:n

Then by the section formula,

The coordinates of the point are,

`((m* x_2+n* x_1)/(m+n), (m* y_2+n* y_1)/(m+n))`

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

=
`((4* 12+1* -8)/(4+1), (4* 0+1* 0)/(4+1))`

=
`((4* 12+1* -8)/(4+1), 0)`

x-coordinate of R =
`(4* 12+1* -8)/(4+1)`

⇒ Location of R =
`(4* 12+1* -8)/(4+1)`

Which is the required expression.