All categories

2 years ago

PQ has a midpoint of M. the coordinates of M are (-4, 7) and the coordinates of P are (2, 13). What are the coordinates of Q?

Mathematics

1 answer:

Natali5045456 [20]2 years ago

3 0

Using the midpoint formula, the coordinates of Q are: <em>A. (-10, 1)</em>

<h3>What is the Midpoint Formula?</h3>

Midpoint formula is given as, $M(x, y) = (\frac{x_2 + x_1}{2} , \frac{y_2 + y_1}{2})$

Thus, given that:

M is the midpoint of PQ.
M (-4, 7)
P (2, 13).

Therefore:

$M(-4, 7) = (\frac{2 + x_1}{2} , \frac{13 + y_1}{2})$

Solve for x-coordinate of P:

-4 = 1/2(2 + x1)

2(-4) = 2 + x1

-8 = 2 + x1

-8 - 2 = x1

x1 = -10

Solve for y-coordinate of P:

7 = 1/2(13 + y1)

14 = 13 + y1

y1 = 1

Therefore, using the midpoint formula, the coordinates of Q are: <em>A. (-10, 1)</em>

<em />

Learn more about the midpoint formula on:

brainly.com/question/88621

You might be interested in

How u do 15f+5g+45 in standard form

ivolga24 [154]

3087810 is 15f+5g+45 in standard form

4 0

3 years ago

What coordinates on the unit circle are associated with the angle measure?

Varvara68 [4.7K]

The tangent of the given angles are the ratios <em>y</em> to the <em>x</em> coordinate of

the point of the terminal side on the unit circle.

The correct options are;

$\dfrac{34 \cdot \pi}{3} \Longleftrightarrow \underline{ \left(-\dfrac{1}{2}, \ -\dfrac{\sqrt{3} }{2} \right)}$

$-\dfrac{7 \cdot \pi}{4} \Longleftrightarrow \underline{ \left(\dfrac{\sqrt{2} }{2}, \ \dfrac{\sqrt{2} }{2} \right)}$

$210^{\circ} \Longleftrightarrow \underline{ \left(-\dfrac{\sqrt{3} }{2}, \ -\dfrac{1}{2} \right)}$

<h3>How to find the points on the unit circle</h3>

The tangent of an angle is given as follows;

$tan (\theta) = \mathbf{ \dfrac{Opposite}{Adjacent}} = \dfrac{\Delta y}{\Delta x}$

First angle

An angle given is; $\mathbf{\dfrac{34 \cdot \pi}{3}}$

Therefore;

$tan \left(\dfrac{34 \cdot \pi }{3} \right) = \mathbf{ \sqrt{3}}$

The above result can be obtained as follows;

$\sqrt{3} = \mathbf{ \dfrac{-\dfrac{\sqrt{3} }{2} }{-\dfrac{1}{2} }}$

Which is obtained when we have;

$\left( \Delta x, \, \Delta y\right) = \mathbf{\left(-\dfrac{1}{2}, \, -\dfrac{\sqrt{3} }{2} \right)}$

Therefore

The required coordinates is therefore;

$\dfrac{34 \cdot \pi}{3} \Longleftrightarrow \left(-\dfrac{1}{2} , \ -\dfrac{\sqrt{3} }{2} \right)$

Second angle

The angle, $\mathbf{-\dfrac{7 \cdot \pi}{4}}$ , gives; $tan \left(-\dfrac{7 \cdot \pi}{4} \right) = 1$

The above value can be obtained as follows;

$\mathbf{\dfrac{\dfrac{\sqrt{2} }{2} }{\dfrac{\sqrt{2} }{2} }} = 1$

Which gives;

$-\dfrac{7 \cdot \pi}{4} \Longleftrightarrow \left(\dfrac{\sqrt{2} }{2}, \, \dfrac{\sqrt{2} }{2} \right)$

Third angle

The angle 210° gives; tan(210°) = $\mathbf{\frac{1}{\sqrt{3} }}$ , which can be obtained as follows;

$\sqrt{ \dfrac{1}{3} } = \mathbf{\dfrac{-\dfrac{1}{2} }{-\dfrac{\sqrt{3} }{2} }}$

Therefore;

$210^{\circ} \Longleftrightarrow \left(-\dfrac{\sqrt{3} }{2}, \ -\dfrac{1}{2} \right)$

Learn more about the unit circle here:

brainly.com/question/1673530

6 0

2 years ago

How is a rational number that is not an integer different from a rational number that is an integer?

lakkis [162]

...huh I don’t get your question

7 0

3 years ago

Algebra 1 question, Please help. Picture attached below ^^

yarga [219]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

If 3x is one factor of 3x²-9x what is the other factor 1. 3x 2. x²-6x 3. x-3 4. x-3

DaniilM [7]

<span>3x²-9x is a binomial, so if you divide it by 3x, the quotient will also be a binomial:

</span><span>3x²-9x
--------- = x - 3 (answer)
3x</span>

4 0

3 years ago