Identify the translation rule on a coordinate plane that verifies that square a(-4, 3), b(-4, 8), c(-9, 3), d(-9, 8) and square a'(-3, 2), b'(-3, 7), c'(-8, 2), d'(-8, 7) are congruent.

 The translation rule that verifies that square A(-4, 3), B(-4, 8), C(-9, 3), D(-9, 8) and square A'(-3, 2), B'(-3, 7), C'(-8, 2), D'(-8, 7) are congruent is

(x, y)  ⇒ (x+1, y-1).

Step-by-step explanation:  We are given to identify the translation rule on a coordinate plane that verifies that

square A(-4, 3), B(-4, 8), C(-9, 3), D(-9, 8) and square A'(-3, 2), B'(-3, 7), C'(-8, 2), D'(-8, 7) are congruent.

We see that the co-ordinates of the vertices of square ABCD and A'B'C'D' are related as follows :

A(-4, 3)  ⇒  A'(-4+1, 3-1) = A'(-3, 2),

B(-4, 8)  ⇒  B'(-4+1, 8-1) = B'(-3, 7),

C(-9, 3)  ⇒  C'(-9+1, 3-1) = C'(-8, 2),

D(-9, 8)  ⇒  D'(-9+1, 8-1) = C'(-8, 7).

Therefore, the required translation rule is given by

(x, y)  ⇒ (x+1, y-1).

Thus, the translation rule that verifies that square A(-4, 3), B(-4, 8), C(-9, 3), D(-9, 8) and square A'(-3, 2), B'(-3, 7), C'(-8, 2), D'(-8, 7) are congruent is

(x, y)  ⇒ (x+1, y-1).

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it