If triangle abc is dilated by a scale factor of 2 with a dilation center of a, what will be the coordinates of point b’?

In the given figure the sides of triangle measures as follows:

AB= 4 units,

BC= 6 units,

Since triangle ABC is right angled triangle, to find AC we will have to use Pythagorean theorem,

AB² + BC² = AC²

Plugging the values of AB and BC to find AC,

4² + 6² = AC²

16+36=AC²

AC = 7.48

Now if the triangle is dilated by a scale factor of 2, each side will be multiplied by 2 to get the new triangle A'B'C'

side A'B' = 2* AB = 2*4= 8 units

side B'C' = 2* BC = 2*6 =12 units

side A'C' = 2*AC = 2*7.48 = 14.96 units

Perimeter of triangle = sum of three sides

Perimeter of triangle A'B'C' = A'B' + B'C' + A'C'= 8+12 + 14.96 = 34.96 units.

Perimeter of triangle ABC = AB+BC + AC = 4+6+7.48 = 17.48 units.

Perimeter of triangle A'B'C' = 2* Perimeter of triangle ABC

The perimeter of new triangle A'B'C' is 34.96 units which is twice that of triangle ABC.

Answer : A) The perimeter of A'B'C' is 2 times the perimeter of ABC.

c. $ 620

Step-by-step explanation:

Given,

Number of friends = 3,

Rent of apartment for a month = $ 650,

So, the total rent for 2 months ( First and last ) = 2 × 650 = $ 1300

Let x be the amount of security they paid,

⇒ Total money paid by them = 1300 + x,

According to the question,

They each paid $ 640,

⇒ Total money paid by them = 3 × 640 = $ 1920

⇒ 1300 + x = 1920

⇒ x = 1920 - 1300 = 620,

Hence, the amount of security deposit was $ 620.