Geometry

Isometries

Translation

         

Point (2,1)(2, 1) is moved to point (10,11)(10,11) by T:(x,y)(x+a,y+b).T: (x, y) \rightarrow (x+a, y+b). What is a+ba+b?

If we translate the point (9,3)(9, 3) by (13,2),(13, 2), what would be the new point?

The curve y=2x2+3x9y=2x^2+3x-9 undergoes a parallel translation by 77 units in the positive direction of the xx-axis and 3-3 units in the positive direction of the yy-axis. If the equation of the resulting curve is y=ax2+bx+c,y=ax^2+bx+c, what is a+b+c?a+b+c?

Consider a translation of axes T:(x,y)(x+a,y+b)T: (x, y) \to (x+a, y+b) such that the coordinates of a point P=(7,4)P=(7, 4) with respect to the new system of coordinates after translation are P=(10,11).P'=(10,-11). What is the value of a+b?a+b?

If the point (m,n)(m,n) is shifted by 66 in the positive xx direction and by 12-12 in the positive yy direction, then it coincides with the center of the circle x2+y26x+2y13=0.x^2+y^2-6x+2y-13=0. What is the value of m+n?m+n?

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