In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.
This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight.
What is slope or gradient?
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What is slope or gradient?
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Calculating the slope or gradient
A line can be defined as a connection of two points.
Slope or gradient which can usually be represented by a small letter (m) is visualized or describes the steepness of the line and can be calculated as follows:
m = ΔY-axis ÷ ΔX-axis
Δ Y-axis = Ya - Yb
Δ X-axis = Xa - Xb
Given two points in a straightline, point A (-2, 0) and point B (4, 3),
ΔY-axis = 3 - 0
ΔY-axis = 3
ΔX-axis = 4 - (-2)
ΔX-axis = 4 + 2
ΔX-axis = 6
Now we can find the gradient:
m = ΔY-axis ÷ ΔX-axis
m = 3 ÷ 6
m = 0.5
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Finding the equation of Line.
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Finding the equation of the Line (y= mx + c)
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Finding the length between two points of a line
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Finding the length
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Finding the Midpoint
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Finding the Midpoint
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The two points below, are found in a straight line. Find the gradient or slope of the line.
Your answer into two decimal places.
(0;0), (0; 0)
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Chances: 3
You get three chances for this question.
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Now, find the equation of the line
Your answer into two decimal places.
(0;0)
✔️❌
Chances: 3
You get three chances for this question.
×
Find length between the points.
Your answer into two decimal places.
(0;0), (0; 0)
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Chances: 2
You get two chances for this question.
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Find Midpoint coordinates.
Your answer into two decimal places.
(0;0), (0; 0)
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Chances: 2
You get a maximum of two chances for this question.
The first question you got 0/3
The second question you got 0/3
The third question you got 0/2
The fourth question you got 0/2
Your total is therefore, 0/0.
Percentage
%
A Message here
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Perpendicular and parallel line slopes
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Perpendicular and parallel line slopes
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Parallel vs Perpendicular lines
Parallel lines
Parallel lines are lines in the same plane that go in the same direction and never intersect no matter how far you extend them in any given direction
Parallel lines always have the same gradient.
Perpendicular lines
perpendicular lines are defined as two lines that meet or intersect each other at right angles .
The slopes of two perpendicular lines are negative reciprocals of each other.
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Introduction to Triangles
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Introduction to Triangles
Triangles aren't just mathematically significant, they are also fundamental to the way we build our environments, both physical and virtual.
Triangles are special because they are exceptionally strong.
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Understand Triangles
A triangle is a three-sided polygon.
The three sides are connected with each other end to end at a point, which forms the angles of the triangle.
The sum of all three angles of the triangle is equal to 180 degrees.
Understanding triangles is very important in both Geometry and Trigonometry.
Classification of triangles
Triangles can be classified by either their angles or sides.
Classification with angles
An acute triangle is a triangle with all angles less than 90°.
The right triangle is a triangle with 2 angles less than 90° and one angle equal to 90°.
An obtuse triangle is a triangle with 2 angles less than 90° and one angle greater 90°.
Classification with sides
An equilateral triangle is a triangle with all three sides equal to one another.
An Isosceles triangle is a triangle with only two of the three sides equal to each other.
A scalene triangle is a triangle with none of the three sides equal to one another.
In addition,
The acute triangle can be Scalene, Isosceles, or Equilateral.
But, obtuse and right triangles can either be Scalene or Isosceles, never Equilateral.
Last but definitely not least
The sum of any given triangle angles always adds up to 180°.
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Tangent ratio
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Tangent ratio
The tangent ratio of a triangle is the ratio of the side opposite of an angle to the side adjacent to the angle which is not the hypotenuse.
The hypotenuse will always be the side of a right angle that is across from the right angle.
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In the diagram, A, B, C and D are the vertices of a quadrilateral having AD parallel to BC.
Given A(0; 0), B(0; 0), C(0; 0) and D(x;y).
Determine the equation of AD with your values into two decimal places.
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Chances: 3
You get a maximum of three chances for this question.
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Given A(0; 0), B(0; 0), C(0; 0) and D(x;y).
Find the x-intercept of AD, with your value into two decimal places.
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Chances: 2
You get a maximum of two chances for this question.
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Given A(0; 0), B(0; 0), C(0; 0) and D(x;y).
DC is perpendicular to the coordinates plane and intercepts it at C, find the coordinates of D.
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Chances: 3
You get a maximum of three chances for this question.
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A(0; 0), B(0; 0), C(0; 0) and D(x;y).
If M was a midpoint of DB, what would be the coordinates of M.
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Chances: 3
You get a maximum of three chances for this question.
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A(0; 0), B(0; 0), C(0; 0) and D(x;y).
AD intercepts M at an angle of 90 °. calculate the Angle ABM
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Chances: 3
You get a maximum of three chances for this question.
The first question you got 0/3
The second question you got 0/2
The third question you got 0/3
The fourth question you got 0/3
The fifth question you got 0/3
Your total is therefore, 0/12.
Percentage
%
A Message here
×
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Solve the following: 0/0 x 0/0
Chances: 1
You get one chance for this question.
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Solve the following: 0/0 x 0/0
Chances: 1
You get one chance for this question.
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Solve the following: 0/0 ÷ 0/0
Chances: 1
You get one chance for this question.
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Solve the following: 0/0 + (0)/0
Chances: 2
You get a maximum of two chances for this question.
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Solve the following: 0/0 + 0/0
Chances: 2
You get a maximum of two chances for this question.
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Solve the following: 0/0 - 0/0
Chances: 2
You get a maximum of two chances for this question.
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A a box with a mass of 0kg rests on a flat surface, find the normal acting on the box.
Chances: 2
You get a maximum of four chances for this question.
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Find the static friction of the box, if its coefficient was 0.
Chances: 2
You get a maximum of two chances for this question.
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The box is now pushed horizontal to the right by a force of 0N is moving to the right with an acceleration of 0m/s2, what is the coefficient of the kinetic friction?
Chances: 3
You get a maximum of three chances for this question.
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The box is now pushed at angle of 0° to the right by a force of 0N, Calculate the new normal force.
Chances: 3
You get a maximum of three chances for this question.
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As the box continue to move, what is the acceleration of the box if kinetic friction coeffient was 0.
Chances: 3
You get a maximum of three chances for this question.
