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03 Jul 2018, 09:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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In the figure above, ABCD is a square. What are the coordinates of point B?
(A) (-4,2)
(B) (-2,4)
(C) (-2,6)
(D) (4, -6)
(E) (6,-2)
Attachment:
square.jpg [ 12.91 KiB | Viewed 16539 times ]
03 Jul 2018, 10:48
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Another approach:
Diagonals will intersect at midpoints of the two lines. Let B be (x,y)
So, (x + 0)/2 = (4 + (-6))/2 which gives x = -2
(y + (-4))/2 = (2+0)/2 which gives y = 6
Hence B is (-2,6), Option C.
Diagonals will intersect at midpoints of the two lines. Let B be (x,y)
So, (x + 0)/2 = (4 + (-6))/2 which gives x = -2
(y + (-4))/2 = (2+0)/2 which gives y = 6
Hence B is (-2,6), Option C.
25 Jul 2018, 17:45
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Bunuel
In the figure above, ABCE is a square. What are the coordinates of point B?
(A) (-4,2)
(B) (-2,4)
(C) (-2,6)
(D) (4, -6)
(E) (6,-2)
using either elimination or the "box" method
Eliminate:
• Answers D) (4, -6) and E) (6,-2). Coordinates of B are in Q II (-x,y). D and E have (x, -y)
• Answer A: (-4, 2) is the mirror point for C (4, 2). Not allowed. Square is not symmetric about the axes.
If you were to flip C across the y-axis, its mirror point would be (-4, 2)
C's mirror point across the y-axis cannot be a vertex because the square is not symmetric about the axes.
• Answer B: (-2,4). Distance of B from x-axis MUST be greater than distance of D from x-axis. More than half of the square is in QI and QII.
The y-coordinate of B (the height of B from the x-axis) MUST be greater than D's distance from x-axis. D's distance is 4. B must be > 4
That leaves one answer: (-2, 6)
Answer C
Attachment:
square2018.07.25.jpg [ 35.18 KiB | Viewed 13856 times ]
If geometric figures are not parallel to the x- and y-axes, draw a box around the figure.
Now we have congruent right triangles all around the smaller square.
The side lengths of those triangles are easy to find because they are right triangles whose vertical and horizontal legs can be measured with the x- and y-axes.
From line segment AO = 6 and properties of a square (parallel sides) we know that one segment of a side of large blue-edged square = 6
From line segment DO = 4 and properties of a square we know that the other segment of a blue-edged side = 4
A square inscribed in a square divides the sides of the larger square proportionally
(Pythagorean theorem)
The larger square's sides are in segments of length 6, 4
Right triangle ABX has height 6. By properties of a right triangle (perpendicular legs), point X and point B are collinear.
The y-coordinate of B is 6. That leaves one answer.
(-2, 6)
Answer C
If you wanted to ascertain the x-coordinate, keep in mind the larger square side's a, b, a, b pattern
By properties of a square, Points C and Y MUST have the same x-coordinate.
Both are 4 away from the y-axis.
But segment BY must have length 6 (by property of inscribed square)
In QII, then, the distance of B from the y-axis is (6-4) = 2
Because the vertex is in QII, its x-coordinate is (-2, 6)
. 
