Distance as Radical Between Coordinates (Angle) (Level 4)

This math topic focuses on calculating the distance between two points on a Cartesian grid, using the Pythagorean theorem. Given pairs of coordinates, students determine the distance expressed as a radical (the square root of an integer). Each problem presents different pairs of points, and students must calculate the correct radical value for the distance. Multiple choice answers are provided, facilitating the application of distance formula skills in a structured manner. This topic also reinforces understanding of the Cartesian coordinate system and the application of Pythagorean relationships in geometry.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Cartesian Grid - Distance as Radical Between Coordinates (Angle) Worksheet

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Cartesian Grid - Distance as Radical Between Coordinates (Angle)
1
Find the distance between the given (x,y) points
A LaTex expression showing \text{Point A:} (-2,1) \\ \text{Point B:} (2,-1)
a A LaTex expression showing square root of 10
b A LaTex expression showing square root of 24
c A LaTex expression showing square root of 20
d A LaTex expression showing square root of 32
e A LaTex expression showing square root of 16
f A LaTex expression showing square root of 26
2
Find the distance between the given (x,y) points
A LaTex expression showing \text{Point A:} (2,1) \\ \text{Point B:} (3,-2)
a A LaTex expression showing square root of 1
b A LaTex expression showing square root of 2
c A LaTex expression showing square root of 7
d A LaTex expression showing square root of 4
e A LaTex expression showing square root of 10
f A LaTex expression showing square root of 17
3
Find the distance between the given (x,y) points
A LaTex expression showing \text{Point A:} (-1,2) \\ \text{Point B:} (-3,-3)
a A LaTex expression showing square root of 21
b A LaTex expression showing square root of 33
c A LaTex expression showing square root of 31
d A LaTex expression showing square root of 29
e A LaTex expression showing square root of 15
f A LaTex expression showing square root of 25
4
Find the distance between the given (x,y) points
A LaTex expression showing \text{Point A:} (-2,3) \\ \text{Point B:} (0,1)
a A LaTex expression showing square root of 3
b A LaTex expression showing square root of 5
c A LaTex expression showing square root of 8
d A LaTex expression showing square root of 15
e A LaTex expression showing square root of 7
f A LaTex expression showing square root of 1
5
Find the distance between the given (x,y) points
A LaTex expression showing \text{Point A:} (-3,-1) \\ \text{Point B:} (1,0)
a A LaTex expression showing square root of 10
b A LaTex expression showing square root of 7
c A LaTex expression showing square root of 11
d A LaTex expression showing square root of 14
e A LaTex expression showing square root of 8
f A LaTex expression showing square root of 17
6
Find the distance between the given (x,y) points
A LaTex expression showing \text{Point A:} (1,1) \\ \text{Point B:} (-1,2)
a A LaTex expression showing square root of 10
b A LaTex expression showing square root of 9
c A LaTex expression showing square root of 5
d A LaTex expression showing square root of 1
e A LaTex expression showing square root of 2
f A LaTex expression showing square root of 7
7
Find the distance between the given (x,y) points
A LaTex expression showing \text{Point A:} (0,-3) \\ \text{Point B:} (-2,2)
a A LaTex expression showing square root of 15
b A LaTex expression showing square root of 25
c A LaTex expression showing square root of 39
d A LaTex expression showing square root of 29
e A LaTex expression showing square root of 13
f A LaTex expression showing square root of 45
8
Find the distance between the given (x,y) points
A LaTex expression showing \text{Point A:} (-2,0) \\ \text{Point B:} (-3,3)
a A LaTex expression showing square root of 1
b A LaTex expression showing square root of 5
c A LaTex expression showing square root of 10
d A LaTex expression showing square root of 8
e A LaTex expression showing square root of 13
f A LaTex expression showing square root of 19