Points P, Q and R are collinear such that PQ: QR=2: 3. Point P is located at (1, 3) and point R is located

6 answers
Question:

Points P, Q and R are collinear such that PQ: QR=2: 3. Point P is located at (1, 3) and point R is located at (11, 15) Find:
a. Q(x, y).
b. The midpoint M.

Answers

17. (1.5,9);

18.(-0.3,3.25)

19.(1.06,3.41)

Option A is correct.

Step-by-step explanation:

Coordinates of the mid point of PQ = ( -6 , -3 )

Coordinate of the point P = ( -1, -4 )

We have to find coordinate of point Q(x , y)

We use the Section formula of mid point.

[tex]Coordinate\:of\:Mid-Point=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Thus, we have

[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(-6,-3)[/tex]

[tex]\implies\frac{x_1+x_2}{2}=-6[/tex]    and   [tex]\frac{y_1+y_2}{2}=-3[/tex]

[tex]\implies\frac{-1+x}{2}=-6[/tex]    and   [tex]\frac{-4+y}{2}=-3[/tex]

[tex]\implies-1+x=-12[/tex]    and   [tex]-4+y=-6[/tex]

[tex]\implies x=-12+1[/tex]    and   [tex]y=-6+4[/tex]

[tex]\implies x=-11[/tex]    and   [tex]y=-2[/tex]

So, Coordinate of point Q is ( -11 , -2 )

Therefore, Option A is correct.

Its easier to do on a graphing calculator. But plot these points and then use rise over run to find the midpoitn

The answer would be (1,3)

The coordinates of the midpoint of the line segment is the average of the coordinates of both end points. For this example above, let (x, y) be the coordinates of point Q. 

                     (abscissa)   -6 = (-1 + x) / 2       ; x = -11
                     (ordinate)    -3 = (-4 + y) / 2       ; y = -2

Therefore, the coordinates of point Q is (-11, -2). The answer is letter A. 

The midpoint of PQ : ( - 6 , - 3 ).
P ( - 1, - 4 );  Q ( x , y )
- 6  = ( - 1 + x ) / 2       
- 1 + x = - 12
x = - 12 + 1 = - 11
- 3 = ( - 4 + y ) / 2
- 4 + y = - 6
y = - 6 + 4 = - 2
 A ) Q ( - 11, - 2 )

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