Distance Between Two Points (Grade 10 NSC Matric Mathematics): Quizzes

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Distance Between Two Points
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How is a point written on a coordinate plane?

As an ordered pair (x,y)(x, y)

What is true about the distance between two points?

It is always positive

Which theorem is used to derive the distance formula?

Pythagoras theorem

What is the distance formula for points (x1;y1)(x_1; y_1) and (x2;y2)(x_2; y_2)?

d=(x1−x2)2+(y1−y2)2d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

Why does the order of subtraction not matter in the distance formula?

Because (x1−x2)2=(x2−x1)2(x_1 - x_2)^2 = (x_2 - x_1)^2

Find the distance between S(−2;−5)S(-2; -5) and T(7;−2)T(7; -2).

9.59.5 units

When finding an unknown coordinate given distance, how many solutions are typically possible?

Two possible values

What is the horizontal distance between points (x1;y1)(x_1; y_1) and (x2;y2)(x_2; y_2)?

AC=x2−x1AC = x_2 - x_1

What should you always do first when solving distance problems?

Draw a sketch

Given RS=13RS = 13, R(3;9)R(3; 9), S(8;y)S(8; y), find yy.

y=−3y = -3 or y=21y = 21

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