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2 years ago

What are the coordinates of R on segments QS such that the ratio is 1:2. Q(-6,2) S(5,6)

Mathematics

1 answer:

tester [92]2 years ago

5 0

Given:

The endpoints of a line segment QS are Q(-6,2) and S(5,6).

Point R divides the line segment QS in 1:2.

To find:

The coordinates of point R.

Solution:

Section formula: If a point divides a line segment in m:n, then the coordinates of that point are:

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

It is given that the endpoints of a line segment QS are Q(-6,2), S(5,6) and point R divides the line segment QS in 1:2. So, the coordinate of point R are:

$R=\left(\dfrac{1(5)+2(-6)}{1+2},\dfrac{1(6)+2(2)}{1+2}\right)$

$R=\left(\dfrac{5-12}{3},\dfrac{6+4}{3}\right)$

$R=\left(\dfrac{-7}{3},\dfrac{10}{3}\right)$

Therefore, the coordinates of point R are $\left(\dfrac{-7}{3},\dfrac{10}{3}\right)$ .

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SVETLANKA909090 [29]

Answer:

C ( 11 , -11 )

Step-by-step explanation:

Solution:-

We are given two points in the cartesian coordinate system as:

A ( 3 , -5 ) B ( 13 , -15 )

The point C lies on the line segment from A to B. The ratio of segment given is:

AC / AB = 4 / 5

To solve such type of problems. We will use vector equation of line AC.

To form a vector equation of line representing AB. We will first determine the direction vector ( d ) that is parallel to the line AB as follows:

d = OB - OA

d = < 13 , -15 > - < 3 , -5 >

d = < 10 , -10 >

The fixed point on the line is taken. We will take point A. The vector equation of line from point A to point B is expressed as:

< x , y > = OA + s*d

< x , y > = < 3, -5 > + s* < 10 , -10 >

The above equation satisfies all the points that lies on the line AB. To determine the coordinates of ( C ). We will plug in the appropriate value of parameter ( s ) and evaluate.

So point C is 4/5 th the magnitude of the distance AB from A. Hence, s = 4/5 as follows:

< x , y > = < 3 , -5 > + ( 4/5 ) * < 10 , -10 >

< x , y > = < 3 , -5 > + < 8 , -8 >

< x , y > = < 11 , -11 > ... Answer

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Answer:

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ivanzaharov [21]

Answer <u>(assuming it can be in point-slope form)</u>:

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Step-by-step explanation:

With the given information, we can use the point-slope formula, $y-y_1 = m (x-x_1)$ , to write the equation of the line. Substitute values for the $m$ , $x_1$ , and $y_1$ in the formula to do so.

The $m$ represents the slope, so substitute $\frac{1}{3}$ in its place. The $x_1$ and $y_1$ represent the x and y values of one point the line intersects, so substitute -6 for $x_1$ and -8 for $y_1$ . This gives the following answer and equation (just make sure to convert the double negatives into positives: