Question

Partitioning- finding the endpoint

Answer 1

Values of x and y will be 12 and 5 respectively.

It's given in the question,

• Three points Q, R and S are collinear.
• Coordinates of Q → (2, 0)
• Coordinates of R → (8, 3)
• Coordinates of S → (x, y)
• QR : RS = 3 : 2

Since, expression for the coordinates of a point (h, k) which divides the segment joining points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio of m : n is given by,

h = $\frac{mx_2+nx_1}{m+n}$

k = $\frac{my_2+my_1}{m+n}$

Since, R is a point on segment QS dividing in the ratio of 3 : 2, coordinates of R will be,

$8=\frac{3x+2\times 2}{3+2}$

$8=\frac{3x+4}{5}$

$3x+4=40$

$3x=36$

$x=12$

Similarly, $3=\frac{3y+2\times 0}{3+2}$

$3=\frac{3y}{5}$

$3y=15$

$y=5$

       Therefore, values of x and y will be 12 and 5 respectively.

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