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In die diagram is A(3 ; 4), B en C hoekkunte van AABC - NSC Mathematics - Question 3 - 2024 - Paper 2
Question 3
In die diagram is A(3 ; 4), B en C hoekkunte van AABC. AB is verleng na S. D en F is onderskeidlik die x- en y-afsnitte van AC. F is die middelpunt van AC en die ink... show full transcript
Worked Solution & Example Answer:In die diagram is A(3 ; 4), B en C hoekkunte van AABC - NSC Mathematics - Question 3 - 2024 - Paper 2
Step 1
Toon dat k = \frac{1}{3}.
Answer
To prove that ( k = \frac{1}{3} ), we will use the coordinates of point A(3, 4) in the equation of line AB, which is given as ( y = kx + 3 ). By substituting point A into the equation:
- Substitute ( x = 3 ) and ( y = 4 ): [ 4 = k(3) + 3 ] [ 4 - 3 = 3k ] [ 1 = 3k ] [ k = \frac{1}{3} ]
Thus, we have demonstrated that ( k = \frac{1}{3} ).
Step 2
Bereken die koördinate van B, die x-afsnit van lyn AS.
Answer
To find the coordinates of B, the x-intercept of line AS, we will set ( y = 0 ) in the equation of line AS:
- Start with the line equation of AS.
- Substitute ( y = 0 ): [ 0 = mx + c ] (Assuming you have the slope ( m ) and y-intercept ( c ) determined from previous sections)
- Solve for x to find the coordinates of point B.
Step 3
Bereken die koördinate van C.
Answer
To calculate the coordinates of point C, we will utilize the given equations and the intersection conditions:
- Identify the intersection points of the equations that define lines AC and BC.
- Set the systems of equations: [ y = 2x - 2 \text{ (for AC)} ] and the equation derived for BC.
- Solve the system to find the coordinates of point C.
Step 4
Bepaal die vergelyking van die lyn parallel aan BC en wat deur S(-15 ; -2) gaan.
Answer
To determine the equation of the line parallel to BC going through point S(-15, -2):
- Calculate the slope of line BC (let's denote it as ( m_{BC} )).
- Using point-slope form ( y - y_1 = m(x - x_1) ):
- Substitute S(-15, -2) into the equation: [ y + 2 = m_{BC}(x + 15) ]
- Rearrange to slope-intercept form to finalize the equation.
Step 5
Step 6
As dit verder gegee word dat AC se lengte 6\frac{6}{5} eenhede is, bereken die waarde van Area van AABD en Area van ΔASC.
Answer
For the areas of triangles AABD and ASC:
- For Area of triangle AABD:
[ Area = \frac{1}{2} \times base \times height ]
- Utilize known lengths (e.g., AB as base and height from point D).
- For Area of triangle ASC:
- Use the area formula or base-height approach, ensuring to incorporate the given length of AC.
- Add both areas to find the total as required.