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3 years ago

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The coordinates of the midpoint of segment GH are M (4,3) and the coordinates of one endpoint are G (5,-6)

1 answer:

Mariulka [41]3 years ago

5 0

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ G(\stackrel{x_1}{5}~,~\stackrel{y_1}{-6})\qquad H(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+5}{2}~~,~~\cfrac{y-6}{2} \right)~~=~~\stackrel{\stackrel{midpoint}{M}}{(4,3)}\implies \begin{cases} \cfrac{x+5}{2}=4\\[1em] x+5=8\\ \boxed{x=3}\\ \cline{1-1} \cfrac{y-6}{2}=3\\[1em] y-6=6\\ \boxed{y=12} \end{cases}$

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Please help I don't understand!

Fiesta28 [93]

The triangles given below in the diagram are similar by; D: The SSS Similarity theorem.

<h3>How to interpret similar triangles?</h3>

From triangle similarity theorems, we know that;

If a segment is parallel to one side of a triangle and intersects the other two sides, then the triangle formed is similar to the original and the segment that divides the two sides it intersects is proportional.

Now, from the given diagram, we see the ratio of corresponding sides are congruent as;

45/30 = 54/36 = 36/24 = 1.5

Thus, the triangles are similar by SSS similarity theorem

Read more about Similar Triangles at; brainly.com/question/14285697

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6 0

2 years ago

The locations in a city are mapped out on a grid, where the origin represents the city center. A traffic helicopter travels due

Elenna [48]

Answer:

Helicopter have traveled 5.55 units of distance approximately if it went directly from one location to the other.

Step-by-step explanation:

We are given the following in the question:

A traffic helicopter travels due north and then due east to get to the location at (-3,4) to the location at (7,13).

The attached image shows the path of helicopter.

Distance Formula:

$(x_1,y_1), (x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Distance traveled by helicopter =

$d((-3,4),(-3,13)) + d((-3,13),(7,13))\\\\=\sqrt{(-3+3)^2 + (13-4)^2} + \sqrt{(7+3)^2 + (13-13)^2}\\= 9+10\\= 19 \text{ units}$

If the helicopter goes directly:

$d((-3,4),(7,13))\\\\=\sqrt{(7+3)^2+(13-4)^2}\\\approx 13.45 \text{ units}$

Difference in distances =

$19 - 13.45 = 5.55\text{ units}$

Thus, helicopter have traveled 5.55 units of distance approximately if it went directly from one location to the other.

7 0

4 years ago

Find the area of the regular figure

Veronika [31]

There’s is by diving side and length by siding

7 0

3 years ago

Make w the subject of the formula: P= 7w-10/60

Dmitry [639]

P= 7w-10/60 (I'm assuming the whole thing is over 60)
x60
60p = 7w-10
+10
60p+10 = 7w
/7
60p+10/7 =w ( it's all over 7l

5 0

3 years ago

Can you show the steps on how to get the answer?

Sati [7]

Answer:

Last option; x = 1 or x = -5

Step-by-step explanation:

1. Simplify the equation.

Step 1: Add 7 to both sides.

$4(|2x+4|)-7+7=17+7$
$4(|2x+4|) = 24$

Step 2: Divide both sides by 4.

$\frac{4(|2x+4|)}{4} = \frac{24}{4}$
$|2x+4| = 6$

2. Now that we simplified the equation to this, we have to solve for absolute value. We know either $2x + 4 = 6$ or $2x + 4 = -6$ .

3. (Solving for 1st possibility)

Step 1: Subtract 4 from both sides.

$2x + 4 - 4 = 6-4$
$2x = 2$

Step 2: Divide both sides by 2.

$\frac{2x}{2} = \frac{2}{2}$
$x = 1$

4. (Solving for 2nd possibility)

Step 1: Subtract 4 from both sides.

$2x+4-4=-6-4$
$2x = -10$

Step 2: Divide both sides by 2.

$\frac{2x}{2}= \frac{-10}{2}$
$x = -5$

5. Now that we have the outcomes of both of our possibilities as x = 1 or x = -5, the last option matches with what we got.

8 0

3 years ago