Respuesta :
Answer: The expression that shows the location of R is,
[tex]\frac{4\times 12+ 1\times -8}{4+1}[/tex]
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 [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the ratio m:n
Then by the section formula,
The coordinates of the point are,
[tex](\frac{m\times x_2+n\times x_1}{m+n}, \frac{m\times y_2+n\times y_1}{m+n})[/tex]
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
= [tex](\frac{4\times 12+1\times -8}{4+1}, \frac{4\times 0+1\times 0}{4+1})[/tex]
= [tex](\frac{4\times 12+1\times -8}{4+1}, 0)[/tex]
x-coordinate of R = [tex]\frac{4\times 12+1\times -8}{4+1}[/tex]
⇒ Location of R = [tex]\frac{4\times 12+1\times -8}{4+1}[/tex]
Which is the required expression.
Answer:
Step-by-step explanation:
Answer: 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.
