Chapter 2: Coordinate Geometry Flashcards by Jacob S | Brainscape

Q

What is the length of an interval formula? (also known as Pythagorean theorem)

A

Length of an interval calculates the exact distance of a line.

a^2 + b^2 = c^2

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Q

What is the midpoint of an interval and what is its formula?

A

The midpoint formula calculates the middle point of a line.

x1+x2/2) , (y1+y2/2) = (x,y) (coordinates

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Q

What is the gradient of an interval and what is its formula?

A

The gradient of an interval is used to calculate the slope of a line. Keep in mind that if the slope is moving downwards, the equation is negative.

rise/run = Gradient

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Q

What is ‘the distance formula’ and what is its formula?

A

The distance formula is an equation used to calculate the length of an individual line.

/(x2-x1)^2 + (y2-y1)^2 = length of an interval (/ = square root)

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Q

What is ‘the gradient formula’ and how do you calculate it?

A

The gradient formula is an alternative way of calculating the gradient of an interval (Pythagorean theorem)

y2-y1/x2-x1 = Gradient

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Q

How do you find a parallel line from the formula y = 2x +5

A

You change the y-intercept, but keep the gradient the same

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Q

How do you find the perpendicular line from the formula y = 2x + 5

A

2*m2 = -1

Therefore parallel line equation = y = -1/2x + y-intercept

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Q

What is the general form equation?

A

ax + by + c = 0

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Q

How do you test whether a point lies on a line?

A

You must substitute the points into y = mx + b form

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Q

What is the midpoint of an interval formula?

A

(x1+x2/2 , y1 + y2/2)

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Q

What equation do you use to test whether a point lies on a line?

A

y = mx + v

Where x is on the Right Hand Side (RHS) and y is on the Left Hand Side (LHS).

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Q

How do you find the equation of a line?

A

Find the gradient (through any xy coordinates).
The y-intercept.
y - mx + b

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Q

How do you find the equation of parallel lines?

A

If m1 = m2, then the line is parallel (in y = mx + b).

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Q

How do you find the equation of a perpendicular line?

A

If m1 * m2 = -1, then the line is parallel (in y = mx + b).

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Q

The vertices of a quadrilateral HJKL are H(-8, -5) J(-1, -2) K(2,5) L(-5,2). Find the exact length of the sides of the quadrilateral.

A

HJ = JK = KL = HL = /58

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Q

The vertices of a quadrilateral HJKL are H(-8, -5) J(-1, -2) K(2,5) L(-5,2). Find the gradient of each side of HJKL.

A

Mhj = 3/7
Mjk = 7/3
Mkl = 3/7
Mhl = 7/3

Q

The vertices of a quadrilateral HJKL are H(-8, -5) J(-1, -2) K(2,5) L(-5,2). Find the exact length of the diagonals HK and JL.

A

HK = /200 (or 10/2)
JK = /32 (or 4/2)

Q

The vertices of a quadrilateral HJKL are H(-8, -5) J(-1, -2) K(2,5) L(-5,2). What type of quadrilateral is HJKL.

A

Rhombus.