### Eric Nicholas K's answer to Sonia's Secondary 4 A Maths Singapore question.

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Hi Sonia! Here is what we do to approach the diagram. I have included the relevant diagram to facilitate your understanding of the question. Let me know if you need more explanation on this question.
Date Posted: 11 months ago
Sonia
11 months ago
Hello! a big thank u for this solution:) Howver, may i know when do i know that i need to make a new equation and solve it simultaneously ? (:
Eric Nicholas K
11 months ago
Good afternoon Sonia!

In this case, we only know that the shortest point from A to line BC is when a line passes through A to be perpendicular to line BC at point D.

At this point, however, we do not have the coordinates of D, which we would need to find to obtain the length of AD.

Hence, to find the required coordinates, we will have to form an equation AD based on our knowledge of linear equation forming. The two lines AD and BC must meet at D, and this is when we use the two equations to solve for the coordinates of D.

Unlike the E Maths trigo case which you are immediately given lengths to work out this shortest length, we do not have the other lengths (or even area) to work out this shortest length. We are only given one coordinate to work with, along with the equation of a line. Therefore, this approach is the way to go for such questions.

Hope this helps!
Sonia
11 months ago
Oooo This is challenging haha Thank you so much again !:))