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sineoko [7]
3 years ago
8

Coordinates A (1, 2), B (3, 2) and C (3, 5) are connected to form ΔABC. If ΔDFE is similar to ΔABC, what are the coordinates of

F? D (6,5), E (10,11)

Mathematics
2 answers:
Stolb23 [73]3 years ago
8 0
F(10,5), I hope this helped you

vesna_86 [32]3 years ago
6 0

Answer:

Possible coordinate of F are (10,5) and (6,11)

Step-by-step explanation:

Coordinates A (1, 2), B (3, 2) and C (3, 5) are connected to form ΔABC

First we plot the points on coordinate plane and then draw triangle ABC. Please see the attachment for figure.

If ΔDFE is similar to ΔABC then their corresponding sides are in proportional.

\therefore \frac{AB}{DF}=\frac{AC}{DE}=\frac{BC}{FE}

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

AB=\sqrt{(3-1)^2+(2-2)^2}=\sqrt{4+0}=2

AC=\sqrt{(3-1)^2+(5-2)^2}=\sqrt{4+9}=\sqrt{13}

BC=\sqrt{(3-3)^2+(5-2)^2}=\sqrt{0+9}=3

DE=\sqrt{(10-6)^2+(11-5)^2}=\sqrt{16+36}=2\sqrt{13}

\frac{AC}{DE}=\frac{1}{2}

We can see  ABC is right angle triangle. So, DEF must be right angle triangle because ΔDFE ~ ΔABC

\frac{BC}{FE}=\frac{1}{2}=\frac{3}{6}

\therefore FE=6

\frac{AB}{DF}=\frac{1}{2}=\frac{2}{4}

\therefore DF=4

Thus, Possible coordinate of F are (10,5) and (6,11)

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babymother [125]

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8 0
3 years ago
Show that (3*8*x)^7 = 6^7*4^7*x^7
Sergeeva-Olga [200]

Answer:

24x^7 = 24x^7

Step-by-step explanation:

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Right side of the equation: 6 times 4 times X = 24x

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2 years ago
Write an<br> algebraic expression fh each verbal expression.
PtichkaEL [24]

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Step-by-step explanation:

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4 0
3 years ago
What is the answer to <br> 24=3(n−5)
-Dominant- [34]
3(n - 5) = 24

Distributive property

3*n = 3n
3*5 = 15

3n - 15 = 24
      + 15  +15

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5 0
3 years ago
In an obtuse isosceles triangle the angle measurements are, x∘, x∘, and (10x−2)=128∘. Find the measurement of one of the acute a
klemol [59]

Answer:

26°

Step-by-step explanation:

An obtuse triangle is a triangle that has one obtuse angle. Obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees.

An isosceles triangle is a triangle that has two equal sides and angles.  

Therefore, an obtuse isosceles triangle is a triangle with an obtuse angle and two equal sides that have two equal acute angles (angle less than 90° ).

Given:

The three angles of the triangle are given to be x°, x°  and (10x−2) = 128°. The obtuse angle is 128°, the two x° are acute angles. We are not using equation 10x − 2 since the value of the obtuse angle has been given as 128°

The sum of angles in a triangle is 180°

∴  x° + x° + 128° = 180°

2x° = 180° - 128°

2x° = 52°

x° = 52° / 2

x° = 26°

The measurement of one of the acute angles is 26°

7 0
2 years ago
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