In die diagram is die vergelyking van lyn AF y = -x - 11 - NSC Mathematics - Question 3 - 2023 - Paper 2

The angle α can be calculated using the tangent function:

an α = rac{(-1) - (-10)}{(-1) - (-1)} = 1 \ α = 135°

Therefore, the size of angle α is 135°.

To find the gradient m of line AC, we can use:

m_{AC} = rac{y_C - y_A}{x_C - x_A} = rac{(10) - (-10)}{(4) - (-1)} = rac{20}{5} = 4

The gradient of line AC is approximately 2.

To determine the equation of line AC:

• We know the gradient m = 2, and we can use point A to find k:

$$y - y_1 = m(x - x_1) \ y - (-10) = 2(x - (-1)) \ y + 10 = 2(x + 1) \ y = 2x - 8$$

Thus, the equation of the line is $y = 2x - 8$.

We can find the coordinates of point C by substituting x = 4 into the equation of line AC:

$$C(4, y) \ y = 2(4) - 8 = 0 \ So, C(4, 0).$$

To find the angle ḞED, we have:

1. $\angle EAB = 63.43°$ (given).
2. Use the fact that opposite angles are equal: $angle = 63,43° So, angle ḞED = 63.43°.

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To find the equation of the circle centered at G and passing through point B:

• The center is G(x=-11, y=19), and point B(4, 5).
• The equation of the circle is:

(x - x_G)^2 + (y - y_G)^2 = r^2 \ = r^2 = ((4 - (-11))^2 + (5 - 19)^2) = r^2 $$. Thus, we express it as:

(x + 11)^2 + (y - 19)^2 = r^2.

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