Introduction to Three Dimensional Geometry

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Step 1: On the xy-plane, the z-coordinate becomes 0, so the foot is D(2,4,0). Step 2: On the yz-plane, the x-coordinate becomes 0, so the foot is E(0,4,5). Step 3: On the xz-plane, the y-coordinate be…

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Step 1: A point on the x-axis has y = 0 and z = 0. Step 2: So its coordinates are of the form (x,0,0). Answer: (x,0,0).

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Step 1: A point on the yz-plane has x = 0. Step 2: So its coordinates are of the form (0,y,z). Step 3: The equation of the yz-plane is x = 0. Answer: Coordinates (0,y,z), equation x = 0.

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Step 1: Reflection in the xy-plane changes only the sign of z. So the image is (-3,2,-7). Step 2: Reflection in the yz-plane changes only the sign of x. So the image is (3,2,7). Step 3: Reflection in …

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Step 1: Use the signs of x, y, z. Step 2: ( +, -, - ) corresponds to the VIII octant. Answer: VIII octant.

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Step 1: The signs are ( -, +, + ). Step 2: This matches the II octant. Answer: II octant.

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Step 1: Distance from the y-axis is √(x² + z²). Step 2: Substitute x = 3 and z = 5. Step 3: Distance = √(3² + 5²) = √(9 + 25) = √34. Answer: √34 units.

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Formula: PQ = √((x2-x1)² + (y2-y1)² + (z2-z1)²). Meaning: P(x1,y1,z1) and Q(x2,y2,z2) are two points in space. Example: For P(2,3,5) and Q(4,3,1), PQ = √((4-2)² + (3-3)² + (1-5)²) = √(4 + 0 + 16) = √2…