1. Problem: Predict the coordinates of shape A after transformations. - Reflection in the y-axis changes each point $(x,y)$ to $(-x,y)$. - Rotation of 180° counterclockwise about the origin changes each point $(x,y)$ to $(-x,-y)$. For reflection: - a (4, 8) → a' (-4, 8) - b (8, 4) → b' (-8, 4) - c (8, 12) → c' (-8, 12) - d (16, 4) → d' (-16, 4) - e (16, 12) → e' (-16, 12) For rotation 180°: - a (10, 2) → a' (-10, -2) - b (8, 4) → b' (-8, -4) - c (8, 8) → c' (-8, -8) - d (12, 8) → d' (-12, -8) - e (12, 4) → e' (-12, -4) 2. Problem: Find missing angles $x$, $y$, and $z$ in a triangle with a right angle and a 75° angle. - The sum of angles in a triangle is 180°. - Given one angle is 90° (right angle), another is 75°. - Calculate $x$ as $x = 180° - 90° - 75° = 15°$. - $y$ is the right angle, so $y = 90°$. - $z$ is the base angle adjacent to $y$, so $z = 75°$. 3. Problem: How many circular plates fit on a rectangular tray? - Circumference $c = 50.24$ cm. - Find radius $r$ using $c = 2\pi r$ so $r = \frac{c}{2\pi} = \frac{50.24}{2 \times 3.14} = 8$ cm. - Area of one plate $= \pi r^2 = 3.14 \times 8^2 = 3.14 \times 64 = 200.96$ cm². - Area of tray $= 35 \times 50 = 1750$ cm². - Number of plates $= \frac{1750}{200.96} \approx 8$ plates. 4. Problem: Find area of polygon from scale drawing. - Scale: 0.5 cm = 1 m, so multiply all lengths by 2 to get meters. - Convert sides: - Bottom side: $7 \times 2 = 14$ m - Left side: $7 \times 2 = 14$ m - Right small vertical: $3.2 \times 2 = 6.4$ m - Right bottom horizontal: $3 \times 2 = 6$ m - Upper middle horizontal: $5.5 \times 2 = 11$ m - Top left vertical: $2.5 \times 2 = 5$ m - Diagonal inside polygon: $1.62 \times 2 = 3.24$ m - Break polygon into rectangles and triangles, calculate areas, then sum. - Approximate total area $= 14 \times 14 + 6 \times 6.4 -$ small triangle area. - Total area approximately $196 + 38.4 -$ small triangle area. - Small triangle area $= \frac{1}{2} \times 3 \times 3.24 = 4.86$ m². - Final area $= 196 + 38.4 - 4.86 = 229.54$ m². Answer summary: - a) Reflection coordinates: a'(-4,8), b'(-8,4), c'(-8,12), d'(-16,4), e'(-16,12) - a) Rotation 180° coordinates: a'(-10,-2), b'(-8,-4), c'(-8,-8), d'(-12,-8), e'(-12,-4) - 2) Angles: $x=15^\circ$, $y=90^\circ$, $z=75^\circ$ - 3) Plates fit: 8 - 5) Area of polygon: approximately 229.54 m²