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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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