Question

Find the coordinates of x, y such that the point P (x, y) lies on the line segment joining the points A (1,4) & B (-3,16).

$\bf {Class\:X}$
$\bf {Chapter:\:Coordinate\:Geometry}$​

Answer 1

Step-by-step explanation:

Given,

Point P(x,y) lies on the line segment joining the points A(1,4) and B(-3,16)

Let, the point "P" divides the line segment in the ratio k:1

By section formula,

For "x" coordinate-

$\boxed{\boxed{x = \frac{mx2+nx1}{m+n}}}$

For "y" coordinate -

$\boxed{\boxed{y = \frac{my2+ny1}{m+n}}}$

Here,

m = k, n =1

x1 =1 , y1 =4

x2 =-3, y2 =16

Now,

By sub. the values in formula,

x = $\frac{k(-3)+1(1)}{k+1}$

x = $\frac{-3k+1}{k+1}$

_____________________________

y = $\frac{k(16)+1(4)}{k+1}$

y = $\frac{16k+4}{k+1}$

y = $\frac{4(4k+1)}{k+1}$

Answer 2

Answer: (-2 , 10)

Step-by-Step explanation:

The coordinates of the point, lying on the line segment joining the points A (1,4) and B (-3,16) will be the coordinates of the midpoint of this line segment.

There can be many points lying on the line segment joining the given points, but since the ratio of the line segment, being divided by the point isn't mentioned herein in the question, we will take the coordinate of the midpoint.

Midpoint formula: $\tt {(x, y) = (\frac {x_{1} + x_{2}}{2}, \frac {y_{1} + y_{2}}{2})}$

Midpoint of A(1,4) and B (-3,16):

$\tt {(x, y) = \frac {1-3}{2} , \frac {4+16}{2}}$

(x , y) = (-2 , 10)