Rectangle abcd has coordinates a(−10, 5) , b(10, 5), c(10, 0) , and d(−10, 0) . rectangle a'b'c'd' has coordinates a ′ (−10,−5), b ′ (10,−5) , c'(10, 0) , and d ′ (−10, 0) . rectangle a"b"c"d" has coordinates a ′′ (−2, −1), b ′′ (2, −1) , c"(2, 0) , and d ′′ (−2, 0) . which transformations describe why rectangles abcd and a"b"c"d" are similar? rectangle abcd was reflected across the y-axis and then dilated by a scale factor of 5 to form rectangle a"b"c"d" rectangle abcd was reflected across the x-axis and then dilated by a scale factor of 1 5 to form rectangle a"b"c"d" . rectangle abcd was dilated by a scale factor of 1 5 and then rotated 90° counterclockwise to form rectangle a"b"c"d" rectangle abcd was dilated by a scale factor of 5 and then rotated 90° counterclockwise to form rectangle a"b"c"d" .

The correct transformation that is applied to Rectangle ABCD to get Rectangle A"B"C"D" is:

  Rectangle ABCD was reflected across the x-axis and then dilated by a scale factor of  1 5  to form Rectangle A"B"C"D" .

We are given vertices of rectangle ABCD as:

 A(−10, 5) , B(10, 5), C(10, 0) , and  D(−10, 0) .

Now we reflect the rectangle across the x-axis to get rectangle A'B'C'D' since the rule that is applied to this reflection is:

            (x,y)  → (x,-y)

Hence,

A(-10,5) → A'(-10,-5)

B(10,5) → B'(10,-5)

C(10,0) → C'(10,0)

D(-10,0) → D'(-10,0)

Now this rectangle A'B'C'D' is dilated by a scale factor of 1/5 to obtain rectangle A"B"C"D" ; Since the rule that is applied to this dilation is:

             (x,y) → (x/5,y/5)

Hence, we have:

A'(-10,-5) → A"(-2,-1)

B'(10,-5) → B"(2,-1)

C'(10,0) → C"(2,0)

D'(-10,0) → D"(-2,0)

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc