I have had major trouble with these questions and my teacher won't offer assistance as it is all about working it out yourself from his point of view. There is at the bottom of this forum 3 questions that I have majorly struggled with, and I'm not asking for a free pass as such, just someone with better knowledge than me to offer help or show me the steps to complete these questions. As mentioned in posts before, maths is my worst subject and I would love to improve my grades. If no one can help, what is the best resource to get a better understanding of these type of questions?
Kind Regards
3. The coordinates of the points A, B, C are (0, 2), (4, 0) and (6, −4) respectively.
a. Find the length AB, and the gradient of AB.
b. Show that the equation of the line L, drawn through C parallel to AB is x + 2y + 2 = 0.
c. Find the coordinates of D, the point where L intersects the x axis.
d. Find the perpendicular distance of the point A from the line L.
4. The points P and Q have coordinates (3, −2) and (1, 3) respectively.
a. The line K has equation 4x + 5y − 2 = 0. Verify that P lies on K.
b. The line L through Q has gradient . Show that the equation of L is x − 3y + 8 = 0.
c. The point of intersection of K and L is R. Find the coordinates of R.
d. Draw a neat sketch on a number plane showing P, Q, R, K and L.
e. Find the perpendicular distance of P from L. Leave your answer as a surd.
f. Find the area of the triangle PQR.
5. Q is the point of intersection of the x axis and the line L with equation 2x − 3y = 2.
a. On a number plane draw the line L, marking on it the point Q.
b. On your diagram, indicate the point P(4, 2) which lies on L. Draw the line K through P perpendicular to L.
c. Find the equation of the line K.
d. Without calculating its co-ordinates, indicate a point R on K which is one unit from P. Mark the right angle RPQ on your diagram.
e. Find the distance PQ.
f. Find the area of the triangle QPR.
g. On your diagram shade the region given by x ≥ 0, 2x − 3y ≥ 2.
h. Write down the equation of the straight line which makes an angle of 120° with the positive direction of the x-axis and has a y-intercept of .
Kind Regards
3. The coordinates of the points A, B, C are (0, 2), (4, 0) and (6, −4) respectively.
a. Find the length AB, and the gradient of AB.
b. Show that the equation of the line L, drawn through C parallel to AB is x + 2y + 2 = 0.
c. Find the coordinates of D, the point where L intersects the x axis.
d. Find the perpendicular distance of the point A from the line L.
4. The points P and Q have coordinates (3, −2) and (1, 3) respectively.
a. The line K has equation 4x + 5y − 2 = 0. Verify that P lies on K.
b. The line L through Q has gradient . Show that the equation of L is x − 3y + 8 = 0.
c. The point of intersection of K and L is R. Find the coordinates of R.
d. Draw a neat sketch on a number plane showing P, Q, R, K and L.
e. Find the perpendicular distance of P from L. Leave your answer as a surd.
f. Find the area of the triangle PQR.
5. Q is the point of intersection of the x axis and the line L with equation 2x − 3y = 2.
a. On a number plane draw the line L, marking on it the point Q.
b. On your diagram, indicate the point P(4, 2) which lies on L. Draw the line K through P perpendicular to L.
c. Find the equation of the line K.
d. Without calculating its co-ordinates, indicate a point R on K which is one unit from P. Mark the right angle RPQ on your diagram.
e. Find the distance PQ.
f. Find the area of the triangle QPR.
g. On your diagram shade the region given by x ≥ 0, 2x − 3y ≥ 2.
h. Write down the equation of the straight line which makes an angle of 120° with the positive direction of the x-axis and has a y-intercept of .