Question

show that the points(-5,1),(5,5),(10,7) are collinear and find the equation of the line passing through them

Answer 1

Answer:

plzz give me brainliest ans and plzzzz follow me

Answer 2

The equation of the line passing through the given points is $y=\frac{2}{5}x+3$

Step-by-step explanation:

Let the given points are

A(-5,1), B(5,5), C(10,7)

These points are colinear if

AB + BC = AC

Let us find these AB, BC and AC by using the distance formula.

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Find the distance between A and B

$AB=\sqrt{5+5)^2+(5-1)^2}\\\\AB=\sqrt{10^2+4^2}\\\\AB=\sqrt{116}\\\\AB=2\sqrt{29}$

Find the distance between B and C

$BC=\sqrt{10-5)^2+(7-5)^2}\\\\BC=\sqrt{5^2+2^2}\\\\BC=\sqrt{29}$

Find the distance between A and C

$AC=\sqrt{10+5)^2+(7-1)^2}\\\\AC=\sqrt{15^2+6^2}\\\\AC=\sqrt{261}\\\\AC=3\sqrt{29}$

Now, we can see that

AB + BC

= 2√29 + √29

=3√29

= AC

Hence, the given points are colinear.

The slope of the line joining the points A (-5, 1) and C(10,7) is

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{7-1}{10+5}\\\\m=\frac{6}{15}\\\\m=\frac{2}{5}$

Hence, the equation of the line is

$y=y_1=m(x-x_1)\\\\y-1=\frac{2}{5}(x+5)\\\\y-1=\frac{2}{5}x+2\\\\y=\frac{2}{5}x+3$

#Learn More:

Show that the points A(-3,2),B(1,-2) and C(5,2) or colinear points.

https://brainly.in/question/12062843