Unit 5
7 marks · HardThe point P(2, 3) is transformed onto Q by a translation of and then by a reflection in the x-axis. The coordinates of Q are used as root values of the quadratic equation , where s and p are the sum and product of the coordinates of Q, respectively.
Find the coordinates of Q after both transformations.
Write down the values of s and p.
Solve the quadratic equation for x.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) Translate: (2+5, 3-2) = (7, 1). Reflect in x-axis: (7, -1). Coordinates of Q: (7, -1)
(b) Sum s = 7 + (-1) = 6; Product p = 7 × (-1) = -7
(c) Equation: x^2 - 6x - 7 = 0. Roots are x = 7, x = -1.
Common mistakes: Reversing reflection or translation order; Wrong sign in root sum/product; Not applying transformations correctly
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Translates point P correctly using vector
A1 (a) · 1 mark · Applies reflection in x-axis correctly
M2 (b) · 1 mark · Sums coordinates for s
A2 (b) · 1 mark · Multiplies coordinates for p
M3 (c) · 1 mark · Forms and writes quadratic equation with correct s and p (follow-through)
A3 (c) · 1 mark · Solves quadratic equation for both roots (follow-through)
B1 (c) · 1 mark · Expresses both answers clearly as values of x
Worked solution
a) Translate P(2,3) by (5, -2): (2+5, 3-2) = (7, 1). Reflect in x-axis: (7, -1). Q = (7, -1).
b) s = 7 + (-1) = 6; p = 7 × (-1) = -7
c) Equation: x^2 - 6x - 7 = 0
Factorise: (x-7)(x+1)=0, so x=7 or x=-1