Practice Problems (Junior Cert Mathematics): Flashcards

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Distance formula for two points

(x2x1)2+(y2y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Midpoint formula

(x1+x22,y1+y22)\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)

Slope formula

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Point-slope form of a line

yy1=m(xx1)y - y_1 = m(x - x_1)

Slope-intercept form

y=mx+cy = mx + c

Distance between A(2,3)A(2, 3) and B(5,7)B(5, 7)

55 units

Midpoint of A(2,3)A(2, 3) and B(5,7)B(5, 7)

(3.5,5)(3.5, 5)

Slope through C(1,2)C(1, 2) and D(4,8)D(4, 8)

22

Equation of line through C(1,2)C(1, 2) and D(4,8)D(4, 8)

y=2xy = 2x

Equation: slope 33, yy-intercept 2-2

y=3x2y = 3x - 2

Intersection: 2x+y=42x + y = 4 and xy=1x - y = 1

(53,23)\left(\frac{5}{3}, \frac{2}{3}\right)

What does slope tell us about a line?

How steep it is

What does distance between points tell us?

How far apart they are

What is the midpoint?

The exact middle between two points

What is the intersection of two lines?

The point where they meet

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