The equations are BC: x + 8y = 52 and CD: x - 2y = -2, derived using point-slope form with slopes calculated from the given coordinates of the trapezium.
To find the equations of the lines BC and CD, we can use the point-slope form of the equation, which is given by "y - y₁ = m(x - x₁)," where (x₁, y₁) is a point on the line, and m is the slope.
1. **Equation of BC:**
The slope of BC is given by the difference in y-coordinates over the difference in x-coordinates. So,
The slope of BC (m₃) = (5 - 6) / (12 - 4) = -1 / 8.
Now, using the point-slope form with point B (x_B, y_B) = (4, 6),
y - 6 = (-1/8)(x - 4)
Simplifying,
8(y - 6) = -1(x - 4)
8y - 48 = -x + 4
x + 8y = 52
So, the equation of BC is x + 8y = 52.
2. **Equation of CD:**
Since BC is parallel to AD, CD must also have the same slope. The slope of AD is
The slope of AD (m₂) = (0 - 5) / (2 - 12) = 5 / 10 = 1 / 2.
So, using the point-slope form with point D (x_D, y_D) = (12, 5),
y - 5 = (1/2)(x - 12)
Simplifying,
2(y - 5) = 1(x - 12)
2y - 10 = x - 12
x - 2y = -2
Thus, the equation of CD is x - 2y = -2.