Question

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)

Answer 1

f(10,5), I hope this helped you

Answer 2

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

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 (AB)/(DF)=(AC)/(DE)=(BC)/(FE)`

Using distance formula,
`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`AB=√((3-1)^2+(2-2)^2)=√(4+0)=2`

`AC=√((3-1)^2+(5-2)^2)=√(4+9)=√(13)`

`BC=√((3-3)^2+(5-2)^2)=√(0+9)=3`

`DE=√((10-6)^2+(11-5)^2)=√(16+36)=2√(13)`

`(AC)/(DE)=(1)/(2)`

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

`(BC)/(FE)=(1)/(2)=(3)/(6)`

`\therefore FE=6`

`(AB)/(DF)=(1)/(2)=(2)/(4)`

`\therefore DF=4`

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