A Level Maths: Straight Line Exam Question
Introduction
In this article we are going to explore how to solve the above question which relates to straight line geometry.
What you need to consider
With questions like this it is important to take note of important keywords within the question and in this case it is the work perpendicular.
Remember that for two perpendicular lines m_1 \times m_2=-1
To start you can find the gradient of the line AB
Gradient AB m_1=\frac{4-0}{0–3}=\frac{4}{3}
So the gradient of the line BC, m_2=-\frac{3}{4}
What next
We are asked to find the value of c, and this can be done by finding the equation of the line BC
Using:
\begin{aligned} & y-y_1=m\left(x-x_1\right) \\ & y-0=-\frac{3}{4}(x–3) \\ & 4 y=-3 x-9 \\ & y=-\frac{3}{4} x-\frac{9}{4} \end{aligned}And so the y intercept or the value of c is -\frac{9}{4}
As a question this is not overly difficult but the key is to understand what the question is asking and identifying the keyphrases within the question.
As you embark on your A Level Maths journey you are going to come across a lot of questions and a lot of terms. It is these terms that you need to know and to be able to translate them successfully into the appropriate technique in mathematics.
You need a strong work plan and revision plan when doing A Level Maths as there are many topics that are interlinked.
As with any maths question, the aim is to keep solutions clear and if using a diagram which is especially so with geometry, make it big and clear.
Good Luck!