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( and a across the axis

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

see the explanation            

Step-by-step 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

geometry: triangles

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lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.