Dist/Mdpt
Find the midpoint of the segment joining C(-3, 1) to D(5, 7).
(1, 4)
For the points P(1, -3) and Q(-4, 0), find the gradient of PQ.
m= -3/5
Find the gradient of the line perpendicular to a line with gradient 3/4
m=-4/3
Draw the graph of the line with equation y= -1/3 x + 4.
y-int: 4
x-int: 12
point (6,2)
What is Ms. Fritch's Dog's name?
Maestro
Find the distance between the points A(-3, 2) and B(1, 5).
5 units
Find the gradient of the line with equation:
5x+3y-6=0
m = -5/3
Find the gradient of the line with equation x = 0.
undefined
Draw the graph of the line with equation
5x-2y+1=0
x-int: -1/5 or -0.2
y-int: 1/2 or 0.5
When is Ms. Fritch's tutoring?
Monday and Wednesday
A circle has centre (3, 2) and radius 5. The points A(8, 2) and B(6, -2) lie on the circle.
Find the midpoint of chord AB.
midpoint = (7, 0)
A cable car descends with 16% gradient.
If the cable car travels 300 metres horizontally, how far does it drop vertically?
43 metres
Find the equation of the vertical line through (-6, 1).
x = -6
Determine the equation of the line which passes through (-3, 4) and (3, 1)
x+2y-5=0
OR
y=-1/2x+5/2
Find a given that P(-3, 4), Q(2, 6), and R(7, a) are collinear
a = 8
Torvald gets into a rowboat at A(1,2) on one side of a circular lake. He rows in a straight line towards the other side. He stops in the middle of the lake for a rest, at M(-2,3).
What are the coordinates of the point Torvald is aiming for?
(-5, 4)
Consider points A(6, 8), B(14, 6), C(-1, -3), and D(-9, -1).
Use gradients to show that AB is parallel to DC
Gradient of AB = -1/4
Gradient of DC = -1/4
Since the gradients of AB and DC are equal, AB||DC.
3x + ky=7 and y=3 - 4x are the equations of two lines. Find k if the lines are parallel.
k = 3/4
Use graphical methods to find where the line through A(-5, 0) and B(3, 10) meets the line with equation 3x+2y-7=0
(-1, 5)
Find the equation of the perpendicular bisector of the line segment joining P(7, -1) and Q(-3, 5).
5x-3y-4=0
A point T on the y-axis is 3 units from the point A(-1, 2). Find the possible coordinates of T.
T = (0, 2+sqrt(8)) or T = (0, 2-sqrt(8))
Farmer Huber has a triangular field with corners A(-1, 1), B(1, 5), and C(5, 1). There are gates at M and N, the midpoints of AB and BC respectively. A straight path goes from M to N.
Use gradients to show that the path MN is parallel to AC.
Hint: When in doubt, draw it out!
gradient MN = 0
gradient AC = 0.
Since the gradients are equal, MN||AC.
5x-7y-8=0 and 3x+ky+11=0 are the equations of two lines. Find the value of k for which the lines are perpendicular.
k = 15/7
Two primary schools are located at P(5, 12) and Q(9, 4) on a council map. The local council wishes to zone the region so that children must attend the closest school to their place of residence. What is the equation of the line that forms this boundary?
x-2y+9=0
OR
y=-1/2 x - 9/2
Fully classify the triangle ABC for A(5, -1), B(-2, 3), and C(0, 8).
Scalene