Hexagon defghi is translated 8 units down and 3 units to the right. if the coordinates of the pre-image of point f are
(–9, 2), what are the coordinates of f'?

(–17, 5)
(–6, –6)
(–17, –1)
(–12, –6)

Solution:

Given: Hexagon DEFGHI is translated 8 units down and 3 units to the right.

Coordinates of point F i.e Pre image = (-9,2)

The rule for transformation is

1. If a point (x,y) is translated a units right and b units up ,the coordinate of new point will be = (x +a,y+b)

2. If a point (x,y) is translated a units left and b units up ,the coordinate of new point will be = (x -a,y+b)

3. If a point (x,y) is translated a units right and b units down ,the coordinate of new point will be = (x +a,y-b)

4. If a point (x,y) is translated a units left and b units down ,the coordinate of new point will be = (x -a,y-b)

Using the above rule , the coordinates of F'= (-9+3, 2-8)=(-6,-6)→Option (B)

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2