Question

Determine whether ∆DEF=∆JKL, given that D(2,0), E(5,0), F(5,5), J(3,-7), K(6,-7), and L(6,-2)

Answer 1

Yes , triangle DEF is congruent to JKL

Explanation:

Given:

The coordinates of triangle DEF are;

D (2, 0)

E(5. 0)

F(5, 5)

and

the coordinates of triangle JKL are:

J(3, -7)

K(6, -7)

L (6, -2)

The rule of translation is used on triangle DEF to get triangle JKL:

`(x , y) \rightarrow (x+1 , y-7)`

i.e

`D (2, 0) \rightarrow (2+1 , 0-7) = (3, -7)` = J

`E (5, 0) \rightarrow (5+1 , 0-7) = (6, -7)` = K

`F (5, 5) \rightarrow (5+1 , 5-7) = (6, -2)` = L

As, we know that two triangles are known as congruent if there is an isometry mapping one of the triangles to the other.

therefore, triangle DEF congruent to triangle JKL