Question

13) Which of the following algebraic representations would result in a reduction dilation?A. (x,y) → (x,y)B. (x,y) → (-2x, -2y)C. (x,y) →x,0.75y)D. (x,y) → x,y)Triangles JKN and MKL are shown below.MN4

Answer 1

Verify each option

REmember that in a dilation reduction, the size of the figure decreases

option A

(x,y) → (3/2x,3/2y)

Is not a reduction, is an enlargement

Option B

(x,y) → (-2x, -2y)

Is not a reduction, is an enlargement

Option C

(x,y) →(2/3x,0.75y)

Is not a dilation, because the scale factor in x is different to the scale factor y

option D

(x,y) → (1/2x,1/2y)

Is a reduction, because the scale factor is less than 1

therefore

The answer is the option D

Problem 14

In this problem we have that

triangle NJK and triangle LMK are congruent by Angle -Side-Angle

Remember that

If two triangles are congruent, then their corresponding angles and corresponding sides are congruent

Verify each option

is not true

option B

so

option B is true

option C

is not true

Problem 15

JKN and MKL is the same that says NJK and LMK

Remember that

If two triangles are similar, then their corresponding angles are congruent and their corresponding sides are proportional

so

Yes, the triangles are similar

(All congruent triangles are similar)