Sorry but I'm confused at these questions, please answer with the method of how you did it. Thank you x p.s Sorry I know there’s a lot of questions -.- but I really need help /: please please please!!!!
1) Transpose each of the equations to standard form (that is, y=mx+c.) State the x- and y-intercept for each.
2) Find the x and y-intercepts of the following lines.
3) A rhombus has vertices A(1,6), B(6.6), C(-2,2) and D(x,y). The coordinates of D are:
A) (2,-3) B) (2,3) C (-2,3) D (3,2) E (3,-2)
4) A rectangle has vertices A(1,5), B(10.6,z) C(7.6,-6,2) and D(-2,1). Find the value of z
5) Show that the triangle ABC with coordinates A(a,a), B(m,-a) and C(-a,m) is isosceles.
6) Find the equation of the straight line that passes through the midpoint of A (-1,-3) and B (3,-5), and has a gradient of 2/3.
7) Show that the line that passes through the points (-4,9) and (0,3) also passes through the point (6,-6)
8) Show that the lines y=6x-3 and x+6y-6=0 are perpendicular to one another.
9) Determine if AB is perpendicular to CD given the following coordinates,
1) A(4,4), B(-8,5), C(-6,2), D(3,11) 2) A(-4,9), B(2,-6), C(-5,8), D(10,14)
10) Find the equation of the line that passes through the point (-2,7) and is perpendicular to a line with a gradient of 2/3.
11) Find the equations of the following lines.
- Passing through the points (1,-3) and (6,-5)
- Passing through the point (5,-2) and parallel to x+5y+5=0
- Passing through the point (1,6) and parallel to x-3y-2=0
- Passing through the point (-1,-5) and is perpendicular to 3x+y+2=0
12) Find the equation of the line which passes through the point (-2,1) and is:
- Parallel to the straight line with equation 2x-y-3=0
- Perpendicular to the straight line with equation 2x-y-3=0
13) Find the equation of the line that contains the point (1,1) and is:
- Parallel to the straight line that contains 3x-5y=0
- Perpendicular to the straight line with equation 3x-5y=0
14) Find the equation of:
- The vertical line that passes through the point (1,-8)
- The horizontal line that passes through the point (-5,-7)
15) Multiple Choice: The vertical line passing through the point (3,-4) Given by:
- y=-4 b)x=3 c)y=3x-4 d) y=-4x+3 e) x=-4
16) Multiple choice: Which of the following points does the horizontal line given by the equation y=-5 pass through?
a) (-5,4) b) (4,5) c) (3,-5) d) (5,-4) e) (5,5)
17) The triangle ABChas vertices A(9,-2), B(3,6) and C(1,4).
- Find the midpoint of M, BC <— Don’t worry about this one, I know how to find the midpoint. I wrote it down so the next few questions doesn't confuse you.
- Find the gradient of BC
- Show that AM is perpendicular bisector of BC.
- Describe triangle ABC
18) Find the equation of perpendicular bisector of the line joining the points (1,2) and (-5,-4).
19) ABCD is parallelogram. The coordinates of A,B and C are (4,1), (1,-2), and (-2,1) respectively find:
- the equation of AD
- the equation of DC
- the coordinates of D.
20) Show that ABCD is a parallelogram. A(2.5,3.5) B(10,-4), C(2.5,-2.5), D(-5,5)
21) Show that ABCD is a trapezium. A(2,7) B(1,-1) C(-0.6,-2.6) D(-2,3)
22) Multiple Choice: The line that passes through the points (0,-6) and (7,8) also passes through:
- (4,3) b (5,4) c (-2,10) d(1,-8) e(1,4)
23) Multiple Choice: The point (-1,5) lies on a line parallel to 4x+y+5=0. Another point on the same line as (-1,5) is:
a (2,9) b (4,2) c (4,0) d(-2,3) e( 3,-11)
24) Find the equation of the straight line given the following conditions:
- Passes through the point(-1,3) and parallel to y=-2x+5
- Passes through the point (4,-3) and parallel to 3y+2x=-3
25) Determine which pairs of the following straight lines are perpendicular.
26) Find the equation of the straight line that cuts the x-axis at 3 and is perpendicular to the line with equation 3y-6x=12
27) Calculate the value of m for which lines with the following pairs of equations are perpendicular to each other.
- 2y-5x=7 and 4y+12=mx
- 5x-6y=-27 and 15+mx=-3y
28) Multiple Choice: The gradient of the line perpendicular to the line with equation 3x-6y=2 is:
- 3 b) -6 c) 2 d) 1/2 e) -2
29) Multiple Choice: Triangle ABC has a right angle at B. The vertices are A(-2,9), B(2,8) and C(1,z) the value of z is:
- 8 1/4 b) 4 c) 12 d)7 3/4 e)-4
30)The map shows the proposed course for a yacht race. Buoys have been positioned at A(1, 5), B(8, 8) and C(12, 6), but the last buoy’s placement, D(10, w), is yet to be finalised.
a. How far is the first stage of the race, that is, from the start, O, to buoy A?
b. The race marshall boat, M, is situated halfway between buoys A and C. What are the coordinates of the boat?
c. Stage 4 of the race (from C to D) is perpendicular to stage 3 (from B to C). What is the gradient of CD?
d. Find the linear equation that describes stage 4.
e. Hence determine the exact position of buoy D.
f. An emergency boat is to be placed at point E,2/3 of the way from buoy A to buoy D. The coordinates of E are (7, 3). How far is the emergency boat from the hospital, located at H, 2 km North of the start?
NOTE: Diagram for question 30 is in the attachment.
31) Show that the following sets of points form the vertices of a right-angled triangle.
a. A(1, −4), B(2, −3), C(4, −7)
b. A(3, 13), B(1, 3), C(−4, 4)
c. A(0, 5), B(9, 12), C(3, 14)
32) Prove that the quadrilateral ABCD is a rectangle when A is (2, 5), B(6, 1), C(3, −2) and
33) Prove that the quadrilateral ABCD is a rhombus, given A(2, 3), B(3, 5), C(5, 6) and D(4, 4). Hint: The diagonals of a rhombus intersect at right angles.