Distance/Midpoint Formula (Junior Cert Mathematics): Quizzes

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Distance/Midpoint Formula
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What is the distance formula for points A(x1,y1)A(x_1, y_1) and B(x2,y2)B(x_2, y_2)?

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

What is the distance between points A(2,3)A(2, 3) and B(5,7)B(5, 7)?

5 units

What is the order of operations when calculating distance?

Brackets, exponents, then addition

Why should you use brackets when substituting values?

To avoid mistakes, especially with negatives

What is the midpoint formula for points A(x1,y1)A(x_1, y_1) and B(x2,y2)B(x_2, y_2)?

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

What does the midpoint represent?

The point exactly halfway between 2 points

What is the midpoint of the line segment connecting A(2,3)A(2, 3) and B(8,7)B(8, 7)?

(5,5)(5, 5)

How do you find the midpoint's xx-coordinate?

Add the xx-coordinates and divide by 2

In Example 1, what is 9+16\sqrt{9 + 16} equal to?

55

What should you always label when starting these problems?

x1,y1,x2,y2x_1, y_1, x_2, y_2 from the points

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