1. The problem is to create a sample C1 (Coordinate Geometry) question for Sec 3 math midterm in Montreal.
2. A typical C1 problem involves finding the equation of a line, distance between points, or midpoint.
3. Let's create a problem: Find the equation of the line passing through points $A(2,3)$ and $B(5,11)$.
4. Formula for slope $m$ of line through points $(x_1,y_1)$ and $(x_2,y_2)$ is:
$$m=\frac{y_2 - y_1}{x_2 - x_1}$$
5. Calculate slope:
$$m=\frac{11 - 3}{5 - 2}=\frac{8}{3}$$
6. Use point-slope form of line equation:
$$y - y_1 = m(x - x_1)$$
7. Substitute $m=\frac{8}{3}$ and point $A(2,3)$:
$$y - 3 = \frac{8}{3}(x - 2)$$
8. Simplify:
$$y - 3 = \frac{8}{3}x - \frac{16}{3}$$
9. Add 3 to both sides:
$$y = \frac{8}{3}x - \frac{16}{3} + 3$$
10. Convert 3 to fraction with denominator 3:
$$3 = \frac{9}{3}$$
11. Final equation:
$$y = \frac{8}{3}x - \frac{16}{3} + \frac{9}{3} = \frac{8}{3}x - \frac{7}{3}$$
12. So, the equation of the line is:
$$y = \frac{8}{3}x - \frac{7}{3}$$
This is a typical C1 question for Sec 3 math midterm.
Line Equation Dee80E
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