Rectangle LMNP with vertices L(-2, 7), M(2,3), N(0, 1), and P(-4, 5):
(a) Translation: (x, y) - (x + 6, y-8)
(b) Reflection: in the y-axis

L’ is (-4,-1)

M’ is (-8,-5)

N’ is (-6,-7)

P’ is (-2,-3)

Step-by-step explanation:

Here, we want to from new vertices by translation followed by reflection;

When we reflect , we simply change the sign of the x-coordinates if we are reflecting over the y-axis

We proceed as follows;

1. L (-2,7)

Translation will be (-2 + 6, 7-8) = (4,-1)

Reflection will be ( -4,-1)

so L’ is (-4,-1)

2. M (2,3)

Translation will be

(2 + 6, 3-8) = (8,-5)

Reflection will be ( -8,-5)

So M’ is (-8,-5)

3. N (0,1)

translation will be

( 0 + 6, 1-8) = (6,-7)

Reflection will be ; (-6,-7)

4.P (-4,5)

Translation will be (-4 + 6, 5-8)

= (2, -3)

Reflection will be;

(-2, -3)

P’ = (-2,-3)

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value