Jump to a New ChapterIntroduction to the SAT IIIntroduction to SAT II Math ICStrategies for SAT II Math ICMath IC FundamentalsAlgebraPlane GeometrySolid GeometryCoordinate GeometryTrigonometryFunctionsStatisticsMiscellaneous MathPractice Tests Are Your Best Friends
 8.1 The Coordinate Plane 8.2 Lines and Distance 8.3 Lines 8.4 Graphing Linear Inequalities 8.5 Other Important Graphs and Equations

 8.6 Coordinate Space 8.7 Key Formulas 8.8 Review Questions 8.9 Explanations
Coordinate Space
When we add another dimension to the coordinate plane, creating a coordinate space, a new axis must be introduced. Meet the z-axis:
The z-axis is perpendicular to both the x- and y-axes. A point in three dimensions is specified by three coordinates: (x, y, z).
The only questions you’re likely to see that involve three-dimensional coordinate geometry will ask you to calculate the distance between two points in space. There is a general formula that allows you to make such a calculation. If the two points are (x1, y1, z1) and (x2, y2, z2), then the distance between them is:
Determining the distance between two points in coordinate space is basically the same as finding the length of the diagonal of a rectangular solid. In solid geometry, we were given the dimensions of the sides; for coordinate geometry, we have the coordinates of the endpoints of that diagonal.
Try the example problem below:
 What is the distance between the points (4, 1, –5) and (–3, 3, 6)?
Using the formula, the answer is , which approximately equals 13.19. To see this in diagram form, take a look at the figure below:
 Jump to a New ChapterIntroduction to the SAT IIIntroduction to SAT II Math ICStrategies for SAT II Math ICMath IC FundamentalsAlgebraPlane GeometrySolid GeometryCoordinate GeometryTrigonometryFunctionsStatisticsMiscellaneous MathPractice Tests Are Your Best Friends
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