Midpoint of (-2,-1) (-6,12)

Mathematics

1 answer:

Leni [432]1 year ago

6 0

Answer:

(-4, 5.5)

Step-by-step explanation:

1. put your Xs and Ys over 2

2. add them together

3. Divide

4. Simplify

5. Turn fraction into decimal

$m(x.y) \\ m = \frac{x1 + x2}{2} . \: \frac{y1 + y2}{2} \\ m = \: \frac{ - 2 + - 6}{2} . \frac{ - 1 + 12}{2} \\ m = ( - \frac{8}{2} . \frac{11}{2} ) \\ m = ( - 4 \: . \: 5 \frac{1}{2} ) \\ \\ \\ mid = ( - 4 \: \: . \: 5.5)$

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Two lighthouses are located 60 miles from one another on a north-south line. If a boat is spotted S 21o E from the northern ligh

jasenka [17]

Answer:

(A)The northern lighthouse is 8.2 miles closer than the southern lighthouse.

Step-by-step explanation:

The triangle attached represents the given problem.

First, let us determine the distance of the Boat from each of the lighthouse.

In Triangle ABC,

∠A+∠B+∠C=180 degrees

21+∠B+16=180

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Using Law of Sines

$\frac{a}{Sin A}=\frac{b}{Sin B}\\\frac{a}{Sin 21^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\a*sin143=60*sin21\\a=60*sin21\div sin143\\a=35.73 miles$

Similarly

$\frac{c}{Sin C}=\frac{b}{Sin B}\\\frac{c}{Sin 16^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\c*sin143=60*sin16\\c=60*sin16\div sin143\\c=27.48 miles$