The four points are

A(2,4),B(6,4),C(6,6)
and

D(2,6),
and lie in the first quadrant. If we rotate only the axes at an angle of

90
°

lie in the first quadrant. If we rotate only the axes at an angle of in anti-clockwise direction, then the figure obtained by joining the adjacent points is ____.

Question

The four points are

A(2,4),B(6,4),C(6,6)
 and

D(2,6),
 and  lie in the first quadrant. If we rotate only the axes at an angle of

90
    °

lie in the first quadrant. If we rotate only the axes at an angle of in anti-clockwise direction, then the figure obtained by joining the adjacent points is ____.

Accepted Answer

The four points are

A(2,4),B(6,4),C(6,6)
 and

D(2,6),
  lie in the first quadrant. If we rotate only the axes at an angle of

90
    °

in an anti-clockwise direction, then the figure obtained by joining the adjacent points is a rectangle.We have been given the four points

A(2,4),B(6,4),C(6,6)
 and D(2, 6).As the geometry's shape is unaffected by rotating the axes, therefore, there will be no change.Using distance formula, D=x2-x12+y2-y12Calculating the distance of AB,Substituting x2=2, x1=6, y2=4, and y1=4, in the formula,AB=2-62+4-42AB=42AB=4Calculating the distance of BC,Substituting x2=6, x1=6, y2=4, and y1=6, in the formula,BC=6-62+4-62BC=22BC=2Calculating the distance of CD,Substituting x2=6, x1=2, y2=6, and y1=6, in the formula,CD=6-22+6-62CD=42CD=4Calculating the distance of DA,Substituting x2=2, x1=2, y2=6, and y1=4, in the formula,DA=2-22+6-42DA=22DA=2The diagonals of the provided quadrilateral are equal on both sides. Additionally, it can be seen from the coordinates of A, B, and C that AB and BC are parallel to the x- and y-axes, respectively.Therefore, the given quadrilateral is a rectangle.

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The four points are A(2,4),B(6,4),C(6,6) and D(2,6), and lie in the first quadrant. If we rotate only the axes at an angle of 90 ° lie in the first quadrant. If we rotate only the axes at an angle of in anti-clockwise direction, then the figure obtained by joining the adjacent points is ____.