SPM 2021 Add Maths Paper 1, Question 8Coordinate Geometry

Solved on video in English and Bahasa Melayu · Form 4, Coordinate Geometry · 5:30 video

The question

(a)

Diagram 5 shows a straight line AB on a grid, with A(p, q) and B(x, y). It is given that point B divides the line segment AC in the ratio m : n, where C(r, s). Derive the formula for the coordinates of the point that divides the line segment.

(b)(i)

It is given that A(3, 2) and B(6, 0), where B divides AC in the ratio m : n with C(r, s). State the range of values of r and of s if m ≤ n.

(b)(ii)

Find the value of p if the straight line x/6 + y/p = 1 is parallel to AB, where A(3, 2) and B(6, 0).

SPM 2021 Add Maths Paper 1, Question 8: the question as drawn in Eduly's video5:30

Part (a)

Step 1

B divides AC in the ratio AB : BC = m : n. Using similar triangles for the components: (q − y)/(y − s) = m/n and (p − x)/(x − r) = m/n.

Why this step

Drawing the horizontal and vertical gaps makes two similar right-angled triangles, so matching sides keep the ratio m : n. That single idea gives both coordinates.

5 more steps, each with the reason for it, in the full solution

Final answer

((mr + np)/(m + n), (ms + nq)/(m + n))

Where students lose marks

Watch out: derive both coordinates. Many students stop after x and never finish the working for y.

Part (b)(i)

5 more steps, each with the reason for it, in the full solution

Final answer

r ≥ 9, s ≤ −2

Where students lose marks

Watch out: after finding r = 9 and s = −2, check which way each inequality points: r ≥ 9 but s ≤ −2.

Part (b)(ii)

4 more steps, each with the reason for it, in the full solution

Final answer

p = 4

Where students lose marks

Watch out: rearranging x/6 + y/p = 1, multiply by p to get y alone. Mishandling 1/p gives p = 1/4, not 4.

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