Mis the midpoint of AN, A has coordinates (-5,-5) and M has coordinates (3, 4) Find the coordinates of N.

Mathematics

1 answer:

NemiM [27]3 years ago

8 0

Answer:

N(11 , 13)

Step-by-step explanation:

M(3,4) = (x,y)

A(-5, -5) = (x1,y1)

N ( )=(x2,y2)

using midpoint formula;

M(x,y)=(x1 + x2)/2 , (y1 + y2)/2

(3,4)= (-5 + x2)/2 , (-5 + y2)/2

Now;

3 = (-5+x2)/2 4 = (-5 +y2)/2

6 = -5 +x2 8 = -5 +y2

6+5 = x2 8+5=y2

x2=11 y2 = 13

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Step-by-step explanation:

Step 1; We plot the points that fall on the line and that lie on an exact x or y coordinate. The following 4 points are plotted (0.5, 7), (2, 5.5), (2.5, 5) and (3.5, 4). We substitute the values of x in the given equations to see which best describes the model.

Step 2; When y = x + 7.5, we get the coordinates as (0.5, 8), (2, 9.5), (2.5, 10) and (3.5, 11).

When y = -x + 7.5, the coordinates are (0.5, 7), (2, 5.5), (2.5, 5) and (3.5, 4).

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8 0

3 years ago

Determine the unknown angle measures, to the nearest degree, in the diagram provided.

serg [7]

Answer:

a is 53.8°, and b is 36.2°

Step-by-step explanation:

Using sine trig rule:

${ \boxed{ \bf{ \sin(b) = \frac{opposite}{hypotenuse} }}}$

${ \tt{ \sin(b) = \frac{78}{132} }} \\ \\ { \tt{b = { \sin }^{ - 1}( \frac{78}{132} ) }} \\ \\ { \tt{b = 36.2 \degree}}$

Summation of angles of triangle:

${ \tt{a + b + 90 \degree = 180 \degree}} \\ { \tt{a + 36.2 \degree + 90 \degree = 180 \degree}} \\ { \tt{a = (180 - 36.2 - 90) \degree}} \\ { \tt{a = 53.8 \degree}}$