Let the point P have coordinates (p, q, r) and let the equation of the plane be ax + by +cz + d = 0Then the distance from the point to the plane is
abs(ap + bq + cr) / sqrt(a^2 + b^2 + c^2).
To find the x-coordinate of a point on the xy-plane, you look at the horizontal distance of the point from the y-axis. The y-coordinate of a point on the xy-plane is the vertical distance of the point from the x-axis.
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yes
True. The distance formula, which is derived from the Pythagorean theorem, calculates the distance between two points in a plane. When finding the distance between a point ((x, y)) and the origin ((0, 0)), the formula simplifies to (d = \sqrt{x^2 + y^2}), which directly corresponds to the Pythagorean theorem. Thus, in this specific case, the distance formula is indeed equivalent to the Pythagorean theorem.
graph it
To find the x-coordinate of a point on the xy-plane, you look at the horizontal distance of the point from the y-axis. The y-coordinate of a point on the xy-plane is the vertical distance of the point from the x-axis.
To find the distance from a point to a plane, you can use the formula ( d = \frac{|Ax_0 + By_0 + Cz_0 + D|}{\sqrt{A^2 + B^2 + C^2}} ), where ( Ax + By + Cz + D = 0 ) is the equation of the plane, and ( (x_0, y_0, z_0) ) are the coordinates of the point. This formula calculates the perpendicular distance from the point to the plane by substituting the point's coordinates into the plane's equation and normalizing it by the plane's normal vector's magnitude.
another point
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Unless the line is a subset of the plane, the intersection is a point.
True. The distance formula, which is derived from the Pythagorean theorem, calculates the distance between two points in a plane. When finding the distance between a point ((x, y)) and the origin ((0, 0)), the formula simplifies to (d = \sqrt{x^2 + y^2}), which directly corresponds to the Pythagorean theorem. Thus, in this specific case, the distance formula is indeed equivalent to the Pythagorean theorem.
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well, you find the two cooridinates on the plane and then graph them! KINDA EASY!
You use the distance formula.
graph it