# Precalculus

posted by .

The distance between 2 points (z1,Y1) and (x2,y2) is given by d = square root (x1-x2)+ (y1-y2)^2)

a - pick 2 arbitrary points in 3 dimensions, (x1, y1, and Z1) and (x2,y2,z2) and plot these points. Not that there are 0- degrees between the xy, xz, and yz axes.

b- using your sketch from part a, find the distance between these 2 points, generalize the above equation to 3 dimensions.

• Precalculus -

first, the axes are perpendicular, the there are 90°, not 0° between axes.

Second, can't do plots here.
Third, once you have picked your points, just plug them into the 3D version of the formula:

d^2 = (x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2

To see that this is true, consider just the distances in the plane z=z1.

w^2 = (x2-x1)^2+(y2-y1)^2
That's just a diagonal line of length w. To get from (x1,y1,z1) to (x2,y2,z2), consider the right triangle from (x1,y1,z1) to (x2,y2,z1) with length w, and go from there to (x2,y2,z2) of length (z2-z1).

If that's confusing, just look online for references to 3D distances.

http://tonto.stanford.edu/~brian/euclidean_distance_in.html

is a good place to start

## Similar Questions

1. ### algebra

plot points (0,6) and (-3,5) plot points (0,0) and (3,1) how do i graph Get some graph paper. Label the x and y axes. For (0,6), place a mark where x = 0 and y=6. Do simillarly for the other points.
2. ### Algebra

Plot the following points on the given rectangular coordinate system by clicking on the given dots and dragging them. Points to plot: (-3, -2 ) (-1, 0) (1, 2) If you were to connect these points with a line, where would the y-intercept …
3. ### Precalculus

1. Simplify the expression ((5x^-2)/(4x^2))^-2 2. (x)/(x^2-81)-(9)/(81-x^2) = 3. Let (-3,3) and (-6,_2) be points in the Cartesian plane. Find the distance between the points.
4. ### geometry CA

Graph quadrilateral ABCD. Then determine the most precise name for each quadrilateral. 1. A (0, 5), B (–5, 0), C (0, –5), D (5, 0) (1 point) square kite rectangle 2. A (–4, 4), B (3, 4), C (5, 0), D (–2, 0) (1 point) square …
5. ### Precalculus

he distance between 2 points (x1,Y1) and (x2,y2) is given by d = square root (x1-x2)^2 + (y1-y2)^2 a - pick 2 arbitrary points in 3 dimensions, (x1, y1, and Z1) and (x2,y2,z2) and plot these points. Not that there are 90 degrees between …
6. ### c++

Distance between two 3-D points. Given two points in space (3-dimensional), find the distance between them. The user will input the coordinates (x,y,z) of the two points and your program will calculate and display the distance between …
7. ### GEOMETRY

POINTS M,N, AND O ARE 3 POINTS ON A LINE WITH COORDINATE 5, 2 SQUARE ROOT OF 5 AND 3 SQUARE ROOT OF 2 RESPECTIVELY, WHICH POINT IS BETWEEN THE OTHER TWO ?
8. ### Math

1. the points given are two of the 3 vertices of a right triangle. Which could be the third vertex of the triangle given 2 points are (-4,-5) & (3,2) ?
9. ### Geometry 1 question

Find the distance between the points C(0, 0) and D(8, 3). 8.3 11 square root of 73 square root of 55 Really don't know. Please help! Thanks
10. ### Math

Calculate the perimeter of the triangle formed by the middle points of the sides of the triangle formed by points A(-8,6) B (2,5) and C (1,7) I've already got the distance between all the points given but I do not know what to do next. …

More Similar Questions

Post a New Question