Directed line segment PT has endpoints whose
coordinates are P(-2, 1) and 1(4,7). Determine
the coordinates of pointſ that divides the segment
in the ratio 2 to 1.

Answer:

(2 , 5)

Step-by-step explanation:

point (x,y) that divides the segment   PI in the ratio 2 to 1

PD=4 - (-2) = 6     PE/ED=2/1     PE=2ED      PE+ED=6    3ED=6    ED=2   PE=4

coordinate of E (2,1)   .... 2 is x coordinate of E

DI=7-1=6    DF/FI=2/1     DF=4

coordinate of F (4,5)   .... .... 5 is y coordinate of E

CF // PD            PC/CI=DF/FI=2/1

C (2,5)

  Coordinates of the point intersecting segment PT in the ratio of 2 : 1 will be (2, 5).

   Given in the question,

   If the endpoints of a segment PQ have been given as[tex]P(x_1,y_1)[/tex] and [tex]Q(x_2,y_2)[/tex] and a point [tex](h,k)[/tex] divides this segment in the ratio of m : n,

[tex]h=\frac{mx_2+nx_1}{m+n}[/tex]

[tex]k=\frac{my_2+ny_1}{m+n}[/tex]

    If the extreme ends of a segment PT are [tex]P(-2,1)[/tex] and [tex]T(4,7)[/tex] and a point (h, k) divides this segment in ratio of 2 : 1,

[tex]h=\frac{2(4)+1(-2)}{2+1}[/tex]

[tex]h=2[/tex]

[tex]k=\frac{2(7)+1(1)}{2+1}[/tex]

[tex]k=5[/tex]

   Therefore, coordinates of the point intersecting segment PT in the ratio of 2 : 1 will be (2, 5).

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