To determine the coordinates of the image of point B after a translation of 2 units to the left and 3 units down, we need to subtract 2 from the x-coordinate and subtract 3 from the y-coordinate of point B.

Given that the original coordinates of point B are (4, 5), the translation results in:
New x-coordinate: 4 - 2 = 2
New y-coordinate: 5 - 3 = 2

Therefore, the image of point B after the translation is (2, 2).

To translate a shape two units to the left, we need to subtract 2 from the x-coordinates of each vertex of the shape.

Given the coordinates of rectangle MNPQ:
M (-3, 3), N (6, 3), P (6, -2), and Q (-3, -2)

To translate the rectangle two units to the left, we subtract 2 from the x-coordinates:
M (-3 - 2, 3), N (6 - 2, 3), P (6 - 2, -2), and Q (-3 - 2, -2)

Simplifying the coordinates, we get:
M (-5, 3), N (4, 3), P (4, -2), and Q (-5, -2)

The matrix addition required to perform this translation is:
| -5 | | -3 | | -2 |
| 3 | + | 3 | = | 3 |
| 1 | | -2 | | -4 |
| -2 | | -2 | | -4 |

Therefore, the matrix addition that would translate rectangle MNPQ two units to the left is:
|-5 -3|
| 3 3 |
| 1 -2 |
|-2 -2 |

To find the area of sector AOB, use the formula:
Sector Area = ( / 360) × × r²
Given:
Diameter = 8 meters Radius = 4 meters
Central angle ( ) = 47°
Now calculate:
Sector Area = (47 / 360) × × 4²
= (47 / 360) × × 16
= 0.1306 × 3.1416 × 16
= 0.1306 × 50.2656
= 6.56
Answer:6.6 square meters

An isosceles trapezoid has one line of symmetry.

radius = diameter / 2 = 6 inches / 2 = 3 inches.
Now, substitute the value of the radius into the formula:
Surface Area = 4 (3 inches)² = 4 (9 square inches) = 36 square inches.
To get the approximate value, we can use the approximation 3.14:
Surface Area 36 × 3.14 113.04 square inches.