Answer:
[tex]P(x,y) = (0,7)[/tex]
Step-by-step explanation:
Given
[tex]J = (-4,11)[/tex]
[tex]K = (8,-1)[/tex]
[tex]JP:JK = 1/3[/tex]
Required
Determine the coordinates of P
[tex]JP:JK = 1/3[/tex]
Represent as ratio
[tex]JP:JK = 1:3[/tex]
Next, is to determine [tex]JP:PK[/tex]
[tex]PK = JK - JP[/tex]
So,
[tex]JP : PK = 1 : 3 -1[/tex]
[tex]JP : PK = 1 : 2[/tex]
The coordinates of P can be calculated using:
[tex]P(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
In this case:
[tex](x_1,y_1) = (-4,11)[/tex]
[tex](x_2,y_2) = (8,-1)[/tex]
[tex]m:n = 1:2[/tex]
So:
[tex]P(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
[tex]P(x,y) = (\frac{1 * 8 + 2 * -4}{1 + 2},\frac{1 * -1 + 2 * 11}{1 + 2})[/tex]
[tex]P(x,y) = (\frac{0}{3},\frac{21}{3})[/tex]
[tex]P(x,y) = (0,7)[/tex]
Hence, the coordinates of P: [tex]P(x,y) = (0,7)[/tex]
