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On a coordinate grid PQ , has the endpoints -P(-2, -11) ans Q(13,4) What is the
location of a point R on PQ that is two-fifths of the way from P to Q?

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On a coordinate grid PQ has the endpoints P2 11 ans Q134 What is the location of a point R on PQ that is twofifths of the way from P to Q Answers in pic class=

Respuesta :

Answer:  A. ( 16/7, -47/7)

Step-by-step explanation:

Since, when a point divides a  line having end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex],

in the ratio of m:n,

Then, by the section formula,

The coordinates of the point are,

[tex](\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})[/tex]

Here, a line having end points P(-2, -11) and Q(13,4) is divided by R in the ratio of 2:5,

⇒  [tex]x_1 = -2[/tex],   [tex]y_1 = -11[/tex],   [tex]x_2 = 13[/tex],   [tex]y_2 = 4[/tex],  [tex]m = 2[/tex], [tex]n = 5[/tex],

Hence, the coordinates of point R

= [tex](\frac{2\times -2+5\times -11}{2+5}, \frac{2\times 4+5\times -11}{2+5})[/tex]

= [tex](\frac{-4-55}{7},\frac{8+-55}{7})[/tex]

= [tex](\frac{16}{7},\frac{-47}{7})[/tex]

⇒ Option A is correct.

Answer:

B. (4,-5)

Step-by-step explanation:

We are given the end-points P = (-2,-11) and Q = (13,4).

The point R is located two-fifths on the way from P to Q.

So, we get that, the ratio sides PQ and QR is 2 : 3

Using the Ratio Formula, we have,

The co-ordinates of the point between [tex](x_{1},y_{1})[/tex] and ([tex](x_{2},y_{2})[/tex] having ratio [tex]m_{1}:m_{2}[/tex] are given by,

[tex](\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}})[/tex]

That is we have,

R = [tex](\frac{2\times 13+3\times (-2)}{2+3},\frac{2\times 4+3\times (-11)}{2+3})[/tex]

i.e. R = [tex](\frac{26-6}{5},\frac{8-33}{5})[/tex]

i.e. R = [tex](\frac{20}{5},\frac{-25}{5})[/tex]

i.e. R = (4,-5)

Thus, the co-ordinates of R is (4,-5).

Hence, option B is correct.

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