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3 years ago

Find the midpoint of the line segment whose endpoints are given (3/5 , -6/7),(2/5,5/7)

Mathematics

1 answer:

snow_lady [41]3 years ago

3 0

The formula of a midpoint between E and F:

$M_{EF}\left(\dfrac{x_E+x_F}{2};\ \dfrac{y_E+y_F}{2}\right)$

We have the points $\left(\dfrac{3}{5},\ -\dfrac{6}{7}\right)$ and $\left(\dfrac{2}{5},\ \dfrac{5}{7}\right)$ . Substitute:

$\dfrac{\frac{3}{5}+\frac{2}{5}}{2}=\dfrac{\frac{5}{5}}{2}=\dfrac{1}{2}\\\\\dfrac{-\frac{6}{7}+\frac{5}{7}}{2}=\dfrac{-\frac{1}{7}}{2}=-\dfrac{1}{7}\cdot\dfrac{1}{2}=-\dfrac{1}{14}$

Answer: $\boxed{\left(\dfrac{1}{2},\ -\dfrac{1}{14}\right)}$

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3 years ago

The midpoint M of CD has coordinates (2, 5). Point C has coordinates (4, 3). What are the coordinates of point D?

AlekseyPX

The coordinates of point D is (0, 7)

<h3><u>solution:</u></h3>

The midpoint M of CD has coordinates (2, 5)

Point C has coordinates (4, 3)

To find: coordinates of point D

The midpoint of line AB conatining points $(x_1, y_1)$ and $(x_2, y_2)$ is given as:

$\text {midpoint}(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here in this problem,

Midpoint (C, D) = (2, 5)

$point C (x_1, y_1) = (4, 3)$

$\text {point } D\left(x_{2}, y_{2}\right)=?$

Subsituting the values in formula we get,

$(2,5)=\left(\frac{4+x_{2}}{2}, \frac{3+y_{2}}{2}\right)$

On comparing both the sides we get,

$2=\frac{4+x_{2}}{2} \text { and } 5=\frac{3+y_{2}}{2}$

$\begin{array}{l}{4=4+x_{2} \text { and } 10=3+y_{2}} \\\\ {\text {Therefore } x_{2}=0 \text { and } y_{2}=7}\end{array}$

Thus the coordinates of point D is (0, 7)

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4 years ago

Find the distance between the points (3, –8) and (0, –9).

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Answer:

B. 3.16

Step-by-step explanation:

1) formula of the required distance is:
$d=\sqrt{(X_A-X_B)^2+(Y_A-Y_B)^2} ;$

2) if A(3;-8) and B(0;-9), then according to the formula above:

$d=\sqrt{(0-3)^2+(-9+8)^2} =\sqrt{10}.$

d≈3.16

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2 years ago