![]() Therefore, the final coordinates are ( –6, 2). Note that the axes are rotated clockwise in this case, but our formulas consider anticlockwise direction. (You may try doing it separately and compare the answers) x = Xcosθ – Ysinθ + h and y = Xsinθ + Ycosθ + k, and solve for X and Y to obtain the new coordinates. We can also combine the two formulas straight away, i.e. We can find the new coordinates by first shifting the origin, followed by rotation, or the other way around. ![]() (iii) We didn’t talk about simultaneous rotation as well as translation. Therefore, the new coordinates will be (5, 0). Now let’s use our formulas x = Xcosθ – Ysinθ and y = Xsinθ + Ycosθ.įinally, on solving for X and Y, we’ll get X = 5 and Y = 0. ![]() They’ll come out to be 4/5 and 3/5 respectively. (ii) In this case, we need to calculate the values of sinθ and cosθ first. Therefore, the coordinates with respect to the shifted origin are (2, 1).Īs simple as that! The next two are equally simple. Solution (i) We’ll directly use the formula derived in the previous lesson: x = X + h, y = Y + k (iii) the origin is shifted to (1, –2), and the axes are rotated by 90° in the clockwise direction. (ii) the axes are rotated by an angle θ anticlockwise, where tanθ = 4/3. (i) the origin is shifted to the point (1, 3). I’ll be closing with a few solved examples relating to translation and rotation of axes.Įxample 1 Find the new coordinates of the point (3, 4) when This will be the last lesson in the Coordinate Geometry Basics series.
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