Question
(a) A rhombus ABCD has a diagonal AC where A is the point (-3, 10) and C is the point (4, -4).
(i) Calculate the length AC.
………………………………………….
(ii) Show that the equation of the line AC is y=-2x+4.
(iii) Find the equation of the line BD.
(b) A curve has the equation\( y=x^{3}+8x^{2}+5x.\)
(i) Work out the coordinates of the two turning points.
(……………….. , ………………..) and (……………….. , ………………..)
(ii) Determine whether each of the turning points is a maximum or a minimum.
Give reasons for your answers.
Answer/Explanation
(a)(i) 15.7 or 15.65…
(ii)\frac{-10-4}{4–3}=-2
10=-2(-3)+c
or -4=-2(4)+c
and correct completion to y=-2x+4.
(iii)\(y=\frac{1}{2}x+\frac{11}{4}\)
(b)(i)\(\left ( -\frac{1}{3},-\frac{22}{7} \right )\) and (-5,50)
(ii)\(\left ( -\frac{1}{3},-\frac{22}{7} \right ) \) minimum
(-5,50) maximum
with correct reasons.
Question
(a) Write down the co-ordinates of A.
( ………………… , ………………….)
(b) Find the equation of line l in the form y=mx+c.
y = ………………………………………..
(c) Write down the equation of the line parallel to line l that passes through the point B.
…………………………………………
(d) C is the point (8, 14).
(i) Write down the equation of the line perpendicular to line l that passes through the point C.
…………………………………………
(ii) Calculate the length of AC.
…………………………………………
(iii) Find the co-ordinates of the mid-point of BC.
( ………………… , ………………….)
Answer/Explanation
(a) (5, 6)
\(y=-\frac{4}{5}x+3\)
(c)\(y=-\frac{4}{5}x-2\)
(d)(i)\(y=\frac{5}{4}x+4\)
(ii) 8.54 or 8.544…
(iii) (4, 6)
Question
A line joins the points A(-3,8) and B(2, -2)
(a)Find the coordinates of the mdipoint of AB.
(b) Find the equation of the line through A and B.
Give your answer in the form y = mx + c.
y = …………………
(c) Another line is parallel to AB and passes through the point (0, 7).
Write down the equation of this line.
(d) Find the equation of the line perpendicular to AB which passes through the point (1, 5).
Give your answer in the form ax + by + c = 0 where a, b and c are integers.
Answer/Explanation
Answer:
(a) (–0.5, 3)
(b) [y = ] –2x + 2 final answer
(c) y = –2x + 7 oe
(d) x – 2y + 9 = 0 or 2y – x – 9 = 0 oe