Cartesian Point Plotting
1. The problem involves plotting given points on two Cartesian planes with different scales.
2. For the first Cartesian plane, the scale is 1 cm representing 5 units for both x and y axes. We plot points A(-3, 12), B(-24, -15), C(0, -7), D(7, 0), E(-29, 0), and F(13, 27).
3. For the second Cartesian plane, the scale is 2 cm representing 5 units for both x and y axes. We plot points G(-3, 7), H(-5, -13), I(2, 19), and J(17, -11).
4. To plot each point, convert units to centimeters using the scale. For the first plane, position in cm equals $\frac{\text{units}}{5}$ cm. For example, point A(-3, 12) in cm is $\left(-\frac{3}{5} \text{ cm}, \frac{12}{5} \text{ cm}\right) = (-0.6 \text{ cm}, 2.4 \text{ cm})$.
5. For the second plane, since 2 cm represents 5 units, position in cm equals $\frac{\text{units} \times 2}{5}$ cm. For example, point G(-3, 7) becomes $\left(\frac{-3 \times 2}{5} \text{ cm}, \frac{7 \times 2}{5} \text{ cm}\right) = (-1.2 \text{ cm}, 2.8 \text{ cm})$.
6. Repeat the calculation for all points on both planes to determine their exact locations for plotting. These calculations help in accurately marking the points on graph paper using the given scales.
Final answer:
- First plane scale: 1 cm = 5 units
- Second plane scale: 2 cm = 5 units
- Coordinates converted to centimeters as shown for correct plotting.