Let E2 be the new system {O, x,y} obtained by rotating the (O, x, y} perpendicular coordinate system arounf the point O in the Euclidean plane. Accordingly, the point {O, Whic of the following is the coordinate according to the, x,y} system? Analytic geometry.

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Let E2 be the new system {O, x,y} obtained by rotating the (O, x, y} perpendicular coordinate system arounf the point O in the Euclidean plane. Accordingly, the point {O, Whic of the following is the coordinate according to the, x,y} system?  Analytic geometry.

Robert Pina · Accepted Answer

Step 1Given that E2 be the new system {O, x′, y′} obtained by rotating the old system {O, x, y}Which gives perpendicular coordinate system around point O in the euclidean planeStep 2If the axes of old co-ordinate be rotates through an angle O in anti-clockwise direction keeping the origin O fixed. Then the new coordinate in terms of old co-ordinate can be written asx′=xcos⁡θ+ysin⁡θy′=−xsin⁡θ+ycos⁡θFor the given problem we have θ=90∘So, x′=xcos⁡90∘+ysin⁡90∘=yy′=−xsin⁡90∘+ycos⁡90∘=−xSo, the new co-ordinate system is {O, y, −x}

enlacamig · Accepted Answer

Step 1  Start by sketching the coordinate axes. Then sketch a rectangular prism to help find the point in space.  In two-dimensional space, the coordinate plane is defined by a pair of perpendicular axes. These axes allow us to name any location within the plane. In three dimensions, we define coordinate planes by the coordinate axes, just as in two dimensions. There are three axes now, so there are three intersecting pairs of axes. Each pair of axes forms a coordinate plane: the xy-plane, the xz-plane, and the yz-plane.   We define the xy-plane formally as the following set: {(x, y, 0):x, y∈}  Similarly, the xz-plane and the yz-plane are defined as {(x, 0, z):x, z∈}  and {(0, y, z∈}, respectively.  If two points lie in the same coordinate plane, then it is straightforward to calculate the distance between them. We that the distance d between two points (x1, y1) and (x2, y2) in the xy-coordinate plane is given by the formula  d=(x2−x1)2+(y2−y1)2  The formula for the distance between two points in space is a natural extension of this formula.   The Distance between Two Points in Space  The distance d between points (x1, y1, z1) and (x2, y2, z2) is given by the formula  d=(x2−x1)2+(y2−y1)2+(z2−z1)2

Let E2 be the new system \{O,\ x',\ y'\} obtained

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