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DimDanny
The coordinates of rectangle ABCD are A(-3, 6), B(-8, 6), C(-8, 2), D(-3, 2). What are the coordinates of the point of intersection of the diagonals of the rectangle after the rectangle is reflected across the y-axis? Answer (-5.5, -4) (5.5, 4) (2.5, 4) (-5.5, -2)
diagonals intersect at their midpoint, ( (-8+ -2)/2, (6+3)/2) which is (-5, 4½) ...
It might be wrong.... |dw:1338856590145:dw| The point of intersection of the rectangle should be the ''centre'' of the rectangle.. so, the x-coordinate should share the same x-coordinate with the mid-point of AB the y-coordinate should share the same y-coordinate with the mid-point of BC x-coordinate of the intersection point = [(-3)+{-8)]/2 = -5.5 y-coordinate of the intersection point = (6+2)/2 = 4 Since the rectangle is reflection along y-axis, the x-coordinate will become positive So, the point is (5.5, 4)
When you reflect over the x axis, it negates the y coordinate. A'(-8,-6); B' (-2,-6); C' (-2,-3) ; D'(-8,-3) The diagonals bisect each other since it is a rectangle. They intersect at their midpoints. The midpoint of A'C' =( (-8+-2)/2, (-6+-3)/2 )= (-5, -4.5) Hoping this helps!
Here's what I've got from GeoGebra :| E is the intersection of diagonals, while F is the point reflected along y-axis