Regular hexagon ABCDEF is symmetrical about the xaxis and the yaxis in a rectangular coordinate plane, as shown above. If the coordinates of point D are (2,0), what is the area, in square units, of rectangle BCEF?
In the rectangular coordinate system, lines L_{1} and L_{2} intersect at point C. Are the lines L_{1} and L_{2} perpendicular to each other?
(1) The product of the slopes of lines L_{1} and L_{2} is at a distance of 1 unit from 0 on the number line.
(2) Lines x = 0 and y = 0 are the perpendicular bisectors of lines L_{1} and L_{2 }respectively.
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Rectangle ABCD is drawn in the xyplane such that side AB is parallel to the xaxis and the side AD is parallel to the yaxis. What are the coordinates of point D?
(1) The coordinates of point A are (2, 3)
(2) The coordinates of point C are (4, 8)
In a rectangular coordinate plane, AB is the diameter of a circle and point C lies on the circle. If the coordinates of points A and B are (1,0) and (5,0), and the area of triangle ABC is 6√2 square units, which of the following can be the coordinates of point C?
In the xyplane, a circle C is drawn with center at (1, 2) and radius equal to 5. Is line l a tangent to the circle C?
(1) Point A with coordinates (a, b) lies on line l such that a(a2) +b(b4) ≤ 20.
(2) The xintercept of line l is 10.
In the xy–coordinate plane, a line segment is drawn to join the points A (2, 1) and C(4, 3). If point B lies on line segment AC, is AB = BC?
(1) The xcoordinate of point B is 3
(2) The ycoordinate of point B is 2
Of all the points that satisfy the equation x^{2}+ y^{2} =25 approximately what percentage of the points also satisfy the
inequality xy ≥ 0?
In the xyplane, what is the area of the region bounded by y +2x ≥ 3, y –x ≥ 6 and the line, that is perpendicular to x = 0 and passes
through the origin?
The line intersects the yaxis at the point P and the line intersects the yaxis at the
point R. If these two lines intersect at point Q, what is the measure of ∠PQR?
In the xy plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?
(1) The product of the xintercepts of the lines l and k is negative.
(2) The product of the yintercepts of the lines l and k is positive.
In the rectangular coordinate system are the points A and B equidistant from point C (1, 0)?
(1) Points A and B lie on circle R, which passes through origin and has a radius equal to 1.
(2) The bisector of the line segment AB passes through point C
In the xyplane, a trapezium ABCD has one of its parallel sides AB on the xaxis with vertex A at the origin. The xcoordinate of point B is 6 and the length of the smaller parallel side CD is 2 less than the length of the longer parallel side. If the side AD lies on the line with the equation y = x and the area of the trapezium is 5 square units, what is the coordinate of point C?
In the xyplane, two circles C and R are drawn such that Circle C has its center at the origin and radius equal to 5 and Circle R has its center at (2, 3) and radius equal to 5. Which of the following is the equation of the line that passes through the intersection points of circles C and R?
The figure above shows a circle whose diameter AB lies on the xaxis as shown. Triangle ACB is a rightangled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the ycoordinate of point C?
In the xyplane given above, if the parallelogram ABCD has all its sides equal, is ABCD a square?
(1) The lines connecting AC and BD have the product of their slopes equal to 1
(2) Points A and D have the same xcoordinates
What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?
In the xyplane, Region R is bounded by the line segments with equations, 2x + 4y = 20 and x=0, whereas Region P is bounded by the line segments with equations 4x + 2y = 20 and y = 0. If the function A(B) is defined as the area of Region B, what is the value of A(P) – 2A(R)?
In the xyplane, the circle C centered at the origin O is intersected by a line l at two points A and B. A line from O is drawn to AB intersecting AB at point D, such that the product of the slopes of OD and AB is 1. If the line l does not pass through origin and the coordinates of point D are (1, 1), what is the radius of the circle?
(1) The x intercept of line l is 2.
(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.
In the xyplane shown, is the slope of line l nonnegative?
1. The line passes through quadrants II and III.
2. For each pair of coordinates (x,y) lying on line l, the product of x and y is not always nonnegative.
In a rectangular coordinate plane, points A(3,4), B(6,5), C(4,3) and D(2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?
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