△abc is reflected to form △a'b'c' .

the coordinates of point a are (4, 1) , the coordinates of point b are (6, 3) , and the coordinates of point c are (2, 4) .

which reflection results in the transformation of △abc to △a'b'c' ?

reflection across the x-axis.

reflection across the y-axis

reflection across y = x.

reflection across y=−x .

Option B.

Step-by-step explanation:

It is given that △ABC is reflected to form △A'B'C' .

It is given that the vertices of triangle ABC are A(4,1), B(6,3) and C(2,4).

From the given figure it is clear that vertices of triangle A'B'C' are A'(-4,1), B'(-6,3) and C(-2,4).

The relation between preimage and image is defined by the rule

Reflection across y-axis represented by the above rule.

It means the △ABC is reflected across the y-axis to form △A'B'C' .

Therefore, the correct option is B.

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

step-by-step explanation:

descending order means to order the polynomials from the term with the largest exponent to the term with the smallest exponent.  

therefore, the correct answer is d.