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vlada-n [284]
3 years ago
10

8. The endpoints of GH are G(-8, -9) and H(8,3). Find the coordinates of the midpoint M

Mathematics
2 answers:
Ad libitum [116K]3 years ago
7 0

Answer:SEE BELOW

Step-by-step explanation:

Average the X and Y coordinates (X,Y)

X = (-8 + 8)/2 = 0

Y = (-9 + 3)/2 = -3

(X,Y) = (0,-3)

dexar [7]3 years ago
7 0

Step-by-step explanation:

\underline{ \underline{ \text{Given \: points}}} :

  • G ( -8 , -9 ) & H ( 8 , 3 )

\underline{ \underline{ \text{To \: find}}} :

  • Midpoint of the given points

\underline{ \underline{ \text{Solution}}} :

Let the point G ( -8 , -9 ) be ( x₁ , y₁ ) & H ( 8 , 3 ) be ( x₂ , y₂)

\boxed{ \sf{Midpoint = (\frac{x_{1} + x_{2}}{2}} \: , \frac{y_{1} + y _{2}}{2} )}

⟶ \tt{( \frac{ - 8 + 8}{2} \:,  \frac{ - 9 + 3}{2} ) }

⟶ \tt{( \frac{0}{2}  \: , \frac{ - 6}{2}} )

⟶ \tt{(0 \:  ,- 3})

\red{ \boxed{ \boxed{ \tt{Our \: final \: answer :  \boxed{ \tt{(0 \:,  - 3)}}}}}}

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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Determine the ratio in which the point (–6, m) divides the join of A(–3, –1) and B(–8, 9). Also, find the value of m.
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Answer:

Ratio = 3 : 2 and value of m = 5.

Step-by-step explanation:

We are given the end points ( -3,-1 ) and ( -8,9 ) of a line and a point P = ( -6,m ) divides this line in a particular ratio.

Let us assume that it cuts the line in k : 1 ratio.

Then, the co-ordinates of P = ( \frac{-8k-3}{k+1},\frac{9k-1}{k+1} ).

But, \frac{-8k-3}{k+1} = -6

i.e. -8k-3 = -6k-6

i.e. -2k = -3

i.e. k = \frac{3}{2}

So, the ratio is k : 1 i.e \frac{3}{2} : 1 i.e. 3 : 2.

Hence, the ratio in which P divides the line is 3 : 2.

Also, \frac{9k-1}{k+1} = m where k = \frac{3}{2}

i.e. m = \frac{\frac{9 \times 3}{2}-1}{\frac{3}{2}-1}

i.e. m = \frac{27-2}{3+2}

i.e. m = \frac{25}{5}

i.e. m = 5.

Hence, the value of m is 5.

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