Question

If R(x,y) is a point on line segment joining points P(6,-8) and Q(-8,6), prove that x+y+2 = 0​

Answer 1

Step-by-step explanation:

P______|______R___|____Q

(6,-8) (x, y) (-8,6)

x=6+(-8)/2

=6-8/2

= -2/2

=-1

y= -8+6/2

=-2/2

=-1

to prove....x+y+2=0

-1-1+2=0

hence proved

Answer 2

The equation of line segment PQ is x+y+2=0 and R(x,y) is a point on line segment PQ, therefore x+y+2=0.

Step-by-step explanation:

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

It is given that a line segment joining points P(6,-8) and Q(-8,6). So, the equation of line is

$y-(-8)=\frac{6-(-8)}{-8-6}(x-6)$

$y+8=-1(x-6)$

$y+8=-x+6$

$y+8+x-6=0$

$x+y+2=0$

R(x,y) is a point on line segment PQ. So,

$x+y+2=0$

Hence proved.

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