Question

What coordinate for F would make triangle ABC and triangle DEF congruent? Triangle ABC is shown. For triangle ABC, A is at 1, 0, B is at negative 1, 2, C is at 2, 3. Two other coordinates are shown. D is at negative 1, 0, E is at 1, 2.

Answer 1

k let's do this.

Let's trace Triangle ABC, and then do the first two points of Triangle DEF. From this, you can determine that F must be (-2,3) due to ABC being reflected. Congruent = Same shape. So, (-2,3) makes this the same shape.

Answer 2

F (-2,3)

Explanation:

We have been given coordinates of three points of triangle ABC and coordinates of two points of triangle DEF and we are asked to find out point F's coordinates.

Since we know that by SSS congruence corresponding side lengths of two congruent triangles are always of same length.

Upon using distance formula we can see length of AB and DE is
`2√(2)` and side lengths of BC and CA are
`√(10)`. In order ABC to be congruent to DEF side lengths EF and FD must be equal to
`√(10)`.

Upon substituting our given values in distance formula we will get two equations,

`EF=\sqrt((1-x)^(2)+(2-y)^(2))=\sqrt10\\`

`FD=\sqrt((-1-x)^(2)+(0-y)^(2))=\sqrt10\\`

Upon solving these equations we will get that our point F lies on (-2,3)

Therefore, coordinates (-2,3) for point F will make triangle ABC and DEF congruent.