The vertices of ∆abc are a(−4,2),b(6,6),c(2,7). a translation maps point a to point a'(6,−3). if b and c are mapped by the same translation, what are the coordinates of b' and c'?

Part a) The coordinates of B' are (16,1)

Part b) The coordinates of C' are (12,2)

Step-by-step explanation:

we know that

The vertices of ∆ABC are A(−4,2),B(6,6),C(2,7)

A translation maps point A to point A'(6,−3)

so

A(−4,2) > A'(6,−3)

The rule of the translation is

(x,y) > (x+a, y+b)

(−4,2)> (−4+a,2+b)

(−4+a,2+b)=(6,−3)

Solve for a

-4+a=6 > a=6+4=10

Solve for b

2+b=-3 > b=-3-2=-5

The rule of the translation  is

(x,y) > (x+10, y-5)

That means > The translation is 10 units at right and 5 units down

Find the coordinates of point B'

Applying the rule of the translation

B(6,6) > B'(6+10,6-5)

B(6,6) > B'(16,1)

therefore

The coordinates of B' are (16,1)

Find the coordinates of point C'

Applying the rule of the translation

C(2,7) > C'(2+10,7-5)

C(2,7) > C'(12,2)

therefore

The coordinates of C' are (12,2)

answer: a and b

step-by-step explanation:

positive

step-by-step explanation:

the quadrant is facing upwards