Question

Type the correct answer in each box. spell all the correctly, and use numerals instead of words for numbers. If necessary, use /for the fraction bar(s) show that ABC is congruent to A'B'C by a translation of ____ unit(s)____ and a ____ across the axis​

Answer 1

A translation of 2 units at left and a reflection across the x-axis

see the explanation

Explanation:

we know that

A translation and a reflection are a rigid transformation

A rigid transformation not change the size or shape of the figure

A rigid transformation produces congruent figures

In this problem triangle ABC and A'B'C' are congruent

The coordinates of triangle ABC are

A( 8,10),B(10,4),C(2,6)

step 1

Translate triangle ABC by the rule

(x,y) ----> (x-2,y)

That means ---> The translation is 2 units left

A( 8,10) ----> A''(6,10)

B(10,4)-----> B''(8,4)

C(2,6) ----> C''(0,6)

step 2

Apply reflection across the x-axis to triangle A''B''C''

The rule of the reflection across the x-axis is equal to

(x,y) ----> (x,-y)

A''(6,10) ----> A'(6,-10)

B''(8,4) ----> B'(8,-4)

C''(0,6) -----> C'(0,-6)

therefore

A translation of 2 units at left and a reflection across the x-axis