Question

The mid point of the line segment joining the points (-8,-10) and (4,-2) is ​

Answer 1

Coordinate of point P by mid point formula,

We have mid point formula,

P(X,Y)=(

2

x

1

+x

2

,

2

y

1

+y

2

)

⇒(

2

−10−2

,

2

4+0

)=(−6,2)

let the ratio be m:n

Then,

m+n

mx

2

+nx

1

=−6

⇒

m+n

m(−4)+n(−9)

=−6

⇒−4m−9n=−6m−6n

⇒2m=3n

⇒

n

m

=

2

3

The raitio =m:n=3:2

Now, ⇒

m+n

my

2

+ny

1

=2

⇒

2+3

3y+2(−4)

=2⇒3y−8=10

⇒y=

3

18

=6

Answer 2

$\mathcal{\green{\underline{\blue{GIVEN:}}}}$

• We are given two points (-8,-10) and (4,-2)

$\mathcal{\green{\underline{\blue{TO \:\: FIND:}}}}$

• We need to find the midpoint between the two points.

$\mathcal{\green{\underline{\blue{SOLUTION:}}}}$

To find the midpoint, there is a special formula called the midpoint formula.

$\boxed{\bold{\large{a_m,a_n=( \dfrac{x_1+x_2}{2} , \dfrac{y_1+y_2}{2} )}}}$

Where $\bf a_m,a_n$ is the midpoint.

The two points are (-8,-10) and (4,-2). Here,

$\bf x_1= -8, \: x_2=4, \: y_1=-10, \: y_2=-2.$

Thus, substitute:

$\bf \to a_m,a_n=(\frac{-8+4}{2} ; \frac{-10-2}{2} )$

$\boxed{\bold{\large{a_m,a_n=(-2,6)}}}$

$\sf{\red{Answer:}}\\Midpoint = (-2,6)$

$\huge\star\:\:{\orange{\underline{\pink{\mathbf{HOPE \:\: THIS \:\: HELPS \:\: :D}}}}}$