Question

If ABC is congruent to EDF where the coordinates of A(-1,1),B(2,4),and C(3,1) what is The measure of EF

Answer 1

EF is 4 units.

Explanation:

It is given that the two triangles
`\trianlge ABC, \triangle EDF` are congruent to each other i.e.

`\trianlge ABC \cong \triangle EDF`

Coordinates are given as:

A(-1,1)

B(2,4)

C(3,1)

As per the property of congruence, all the corresponding sides and angles of the two triangles are equal to each other.

i.e. AB = ED

BC = DF

AC = EF

We are given with the coordinates of points A, B and C here from which we can easily calculate the side AC using the distance formula.

`Distance = √((x_2-x_1)^2+(y_2-y_1)^2)`

Where
`(x_1,y_1), (x_2,y_2)` are the coordinates of the two points whose distance is to be calculated.

So,

`AC = √((3-(-1))^2+(1-1)^2)\\\Rightarrow AC = √(4^2)\\\Rightarrow AC = 4\ units`

Hence, AC = EF = 4 units