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.
True
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.
another point
True
yes
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.
True
True
well, you find the two cooridinates on the plane and then graph them! KINDA EASY!
graph it
You use the distance formula.
To find the horizontal distance of an object dropped by a plane, you can use the formula: distance = velocity x time. First, calculate the time it takes for the object to fall using the formula: time = √(2 x height / g), where g is the acceleration due to gravity (9.81 m/s^2). Then, multiply the time by the horizontal velocity of the plane to find the horizontal distance the object travels.