1. **Problem:** A fishing boat is at point A (3, 2) and a buoy is at point B (7, 5). Find how far east and north the boat must travel to reach the buoy. 2. **Formula and Explanation:** The eastward distance is the difference in x-coordinates, and the northward distance is the difference in y-coordinates. 3. **Calculation:** - East distance = $7 - 3 = 4$ kilometers - North distance = $5 - 2 = 3$ kilometers 4. **Answer:** The boat must travel 4 kilometers east and 3 kilometers north to reach the buoy. --- 1. **Problem:** Find the quadrant of Navotas City Hall located at (-4, 6). 2. **Explanation:** Quadrants are defined as: - Quadrant I: $x > 0, y > 0$ - Quadrant II: $x < 0, y > 0$ - Quadrant III: $x < 0, y < 0$ - Quadrant IV: $x > 0, y < 0$ 3. **Observation:** Since $x = -4 < 0$ and $y = 6 > 0$, the point is in Quadrant II. 4. **Answer:** Navotas City Hall is in Quadrant II. --- 1. **Problem:** Find the distance between two health centers P (1, 3) and Q (4, 7). 2. **Formula:** Distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Calculation:** $$d = \sqrt{(4 - 1)^2 + (7 - 3)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$ kilometers 4. **Answer:** The distance between the two health centers is 5 kilometers. --- 1. **Problem:** Find the area of the triangular playground with lamp posts at (2, 1), (6, 1), and (2, 5), where 1 unit = 10 meters. 2. **Formula:** Area of a triangle with base $b$ and height $h$ is $$\text{Area} = \frac{1}{2} b h$$ 3. **Calculation:** - Base length between (2,1) and (6,1) is $6 - 2 = 4$ units - Height between (2,1) and (2,5) is $5 - 1 = 4$ units - Convert units to meters: $4 \times 10 = 40$ meters - Area in square meters: $$\frac{1}{2} \times 40 \times 40 = \frac{1}{2} \times 1600 = 800$$ square meters 4. **Answer:** The area of the triangular playground is 800 square meters. --- 1. **Problem:** Find the slope of the road between points (2, 4) and (6, 10). 2. **Formula:** Slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculation:** $$m = \frac{10 - 4}{6 - 2} = \frac{6}{4} = 1.5$$ 4. **Answer:** The slope of the road is 1.5.