8th Grade Distance on the Coordinate Plane Quiz: 10 Questions with Explanations

A 23B 17C 7D 120

64 + 225 = 289, so the distance is 17.

A 14B 8C 10D 100

Legs 6 and 8, hypotenuse 10.

A 5B 7C 4D 25

Legs 3 and 4 give 5.

A \(d = (x_{2} – x_{1}) + (y_{2} – y_{1})\)B \(d = \sqrt{x_{2} – x_{1}} + \sqrt{y_{2} – y_{1}}\)C \(d = (x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2}\)D \(d = \sqrt{(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2}}\)

The sum of the squares must be under a square root.

A 9B 5C 10D 81

The x-coordinates match, so subtract y values: 7 – (-2) = 9.

A 12B 7C 10D 5

3 + 4 + 5 = 12.

A 1B 49C 7D 5

x^2 + 576 = 625, so x^2 = 49.

A \((6, 5)\)B \((5, 5)\)C \((1, 8)\)D \((7, 3)\)

(5,5) gives 50; (6,5) gives 61; (1,8) gives 65; (7,3) gives 58.

A 17 milesB 7 milesC 60 milesD 13 miles

Legs 5 and 12 give hypotenuse 13.

A the area of a circleB the Pythagorean theoremC the slope formulaD the angle sum of a triangle

The legs are the changes in x and y.