Regular hexagon ABCDEF is symmetrical about the x-axis and the y-axis 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 L1 and L2 intersect at point C. Are the lines L1 and L2 perpendicular to each other?
(1) The product of the slopes of lines L1 and L2 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 L1 and L2 respectively.
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Rectangle ABCD is drawn in the xy-plane such that side AB is parallel to the x-axis and the side AD is parallel to the y-axis. 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 xy-plane, 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(a-2) +b(b-4) ≤ 20.
(2) The x-intercept 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 x-coordinate of point B is 3
(2) The y-coordinate of point B is 2
Of all the points that satisfy the equation x2+ y2 =25 approximately what percentage of the points also satisfy the
inequality xy ≥ 0?
In the xy-plane, 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 y-axis at the point P and the line intersects the y-axis 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 x-intercepts of the lines l and k is negative.
(2) The product of the y-intercepts 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 xy-plane, a trapezium ABCD has one of its parallel sides AB on the x-axis with vertex A at the origin. The x-coordinate 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 xy-plane, 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 x-axis as shown. Triangle ACB is a right-angled 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 y-coordinate of point C?
In the xy-plane 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 x-coordinates
What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?
In the xy-plane, 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 xy-plane, 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 xy-plane shown, is the slope of line l non-negative?
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 non-negative.
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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117 videos|122 docs|135 tests
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