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

Answer:

EF is 4 units.

Step-by-step 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.

$Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

So,

$AC = \sqrt{(3-(-1))^2+(1-1)^2}\\\Rightarrow AC = \sqrt{4^2}\\\Rightarrow AC = 4\ units$

Hence, AC = EF = 4 units