Analytic Geometry in Rectangular Coordinates

The field of Analytic Geometry in Rectangular Coordinates is based on the exploration and interpretation of points, lines, and forms within a two-dimensional space through the usage of x and y coordinates. It allows us to delve into the investigation of geometric figures and their characteristics by converting them into algebraic formulas, thereby creating a nexus between algebra and geometry.

Finding the Midpoint of a Line Segment

Find the midpoint of the line segment with endpoints at \((-3, 4)\) and \((5, -2)\).
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Distance Formula

Find the distance between the points A(1, 2) and B(4, 6) in the rectangular coordinate system.
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Calculating Slope and y-Intercept

Given the points A(2,4) and B(6,8), find the slope and y-intercept of the line AB.
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Identifying Conic Sections

Identify the type of the conic section represented by the equation \(9x^2 - 4y^2 = 36\).
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Identifying Circles

QUESTION 10.3 Writing the Equation of a Sphere Given its Center and Radius Choose one $\cdot 5$ points Write the equation of a sphere with center $\vec{c}=(2,1,-5)$ and radius $R=3$ \[ (x-2)^{2}+(y-1)^{2}+(z+5)^{2}=9 \] \[ (z-2)^{2}+(y-1)^{2}+(z+5)^{2}=3 \] \[ (x+2)^{2}+(y+1)^{2}+(z-5)^{2}=9 \]
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Popular Problems

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