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Alinara [238K]
3 years ago
14

The midpoint of a line segment with end points as (-10, y1) and (-6, 7) is (-8, 6). What is the value of y1?

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
8 0
The formulae for the midpoint are correct:

M ( (x₂-x₁)/2 , <span>(y₂-y₁)/2 )

You need to invert these to get x</span>₁ and y₁:
x₁ =2xm - x₂
y₁ =2ym - y₂

Try with the x to prove the formulae are correct:
x<span>₁ =2·(-8) - (-6) = -16 + 6 = -10  which is what we have!

Then, use</span> the other formula for y:
<span>y₁ =2 ·(6) - (7) = 12 - 7 = 5

Therefore y</span>₁ = 5
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Answer:

The correct answer is 450°, 810°, -270° and -630°.

Step-by-step explanation:

According to the given scenario, the calculation of the two positive angles and two negative angles i.e. coterminal is as follows:

The coterminal angles are the angles in which the difference could be 360 degrees or the multiples of 360 degrees

For 90 degrees, the two positive angles are

a. 90° + 360°

= 450°

450° + 360°

= 810°

b. The two negative angles are

= 90° - 360°

= -270°

-270° - 360°

= -630°

3 0
3 years ago
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san4es73 [151]

Answer:

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Step-by-step explanation:

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4 0
3 years ago
I need help for this, thanks
gulaghasi [49]

(a) Yes all six trig functions exist for this point in quadrant III. The only time you'll run into problems is when either x = 0 or y = 0, due to division by zero errors. For instance, if x = 0, then tan(t) = sin(t)/cos(t) will have cos(t) = 0, as x = cos(t). you cannot have zero in the denominator. Since neither coordinate is zero, we don't have such problems.

---------------------------------------------------------------------------------------

(b) The following functions are positive in quadrant III:

tangent, cotangent

The following functions are negative in quadrant III

cosine, sine, secant, cosecant

A short explanation is that x = cos(t) and y = sin(t). The x and y coordinates are negative in quadrant III, so both sine and cosine are negative. Their reciprocal functions secant and cosecant are negative here as well. Combining sine and cosine to get tan = sin/cos, we see that the negatives cancel which is why tangent is positive here. Cotangent is also positive for similar reasons.

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cricket20 [7]

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In the figure below, segment CD is parallel to segment EF and point H bisects segment DE :
Grace [21]

Answer:

See explanation

Step-by-step explanation:

In the figure below, segment CD is parallel to segment EF, DE is a transversal, then angles DIH and HGI are congruent as alternate interior angles when two parallel lines are cut by a transversal.

Consider triangles DIH and EGH. In these triangles,

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Thus,

\triangle DIH\cong \triangle EGH by AAS postulate

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