Question

∆ABC has vertices at A(12, 8), B(4, 8), and C(4, 14). ∆XYZ has vertices at X(6, 6), Y(4, 12), and Z(10, 14). ∆MNO has vertices at M(4, 16), N(4, 8), and O(-2, 8). ∆JKL has vertices at J(14, -2), K(12, 2), and L(20, 4). ____1_____ are congruent. A ___2____ is a single rigid transformation that maps the two congruent triangles.


1- a) triangle ABC and Triangle XYZ
b) triangle ABC and Triangle MNO
c) triangle JKL and Triangle ABC
d) triangle MNO and Triangle XYZ

2- a) reflection
b) dilation
c) rotation
d) translation

Answer 1

Answer:

Option B is correct.

Rotation.

Step-by-step explanation:

Given ∆ABC has vertices at A(12, 8), B(4, 8), and C(4, 14). ∆XYZ has vertices at X(6, 6), Y(4, 12), and Z(10, 14). ∆MNO has vertices at M(4, 16), N(4, 8), O(-2, 8). ∆JKL has vertices at J(14, -2), K(12, 2), and L(20, 4).

we have to tell the two triangles which are congruent.

From the graph we see

AB=MN=8 units

BC=OM=6 units

∠ABC=∠OMN=90°

By SAS rule, ΔABC≅ΔMNO.

Option B is correct.

By distance formula,

$ON=\sqrt{(16-8)^2+(4+2)^2}=\sqrt{100}=10 units$

$AC=\sqrt{(14-8)^2+(4-12)^2}=\sqrt{100}=10 units$

All the three sides are of same length and the triangles are congruent therefore, the rotation is a single rigid transformation that results into two congruent triangles.

Answer 2

Answer:

B is correct

Step-by-step explanation: