Question

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'?

Answer 1

B(16,1)

C(12,2)

Explanation:

In orde to calculate the other points we just have to find the translation on the example so we have to withdraw from AX2 and AY2, AX1 and AY2 respectively:

6-(-4)=+10 on the X axis

-3-2=-5 on the Y axis

Then we just add this to the other points:

B(6,6):

6+10=16

6-5=1

B2=(16,1)

C(2,7)

2+10=12

7-5=2

C2(12,2)

Answer 2

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

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

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)