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Test: Coordinate Geometry- 2 - Question 1

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?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 1

Test: Coordinate Geometry- 2 - Question 2

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.

Detailed Solution for Test: Coordinate Geometry- 2 - Question 2

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Test: Coordinate Geometry- 2 - Question 3

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)

Detailed Solution for Test: Coordinate Geometry- 2 - Question 3

Test: Coordinate Geometry- 2 - Question 4

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?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 4

Test: Coordinate Geometry- 2 - Question 5

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.

Detailed Solution for Test: Coordinate Geometry- 2 - Question 5

Test: Coordinate Geometry- 2 - Question 6

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

Detailed Solution for Test: Coordinate Geometry- 2 - Question 6

Test: Coordinate Geometry- 2 - Question 7

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?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 7

Test: Coordinate Geometry- 2 - Question 8

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?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 8

Test: Coordinate Geometry- 2 - Question 9

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?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 9

Test: Coordinate Geometry- 2 - Question 10

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.

Detailed Solution for Test: Coordinate Geometry- 2 - Question 10

Test: Coordinate Geometry- 2 - Question 11

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

Detailed Solution for Test: Coordinate Geometry- 2 - Question 11

Test: Coordinate Geometry- 2 - Question 12

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?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 12

Test: Coordinate Geometry- 2 - Question 13

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?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 13

Test: Coordinate Geometry- 2 - Question 14

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?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 14

Test: Coordinate Geometry- 2 - Question 15

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

Detailed Solution for Test: Coordinate Geometry- 2 - Question 15

Test: Coordinate Geometry- 2 - Question 16

What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 16

Test: Coordinate Geometry- 2 - Question 17

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)|?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 17

Test: Coordinate Geometry- 2 - Question 18

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.

Detailed Solution for Test: Coordinate Geometry- 2 - Question 18

Test: Coordinate Geometry- 2 - Question 19

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.

Detailed Solution for Test: Coordinate Geometry- 2 - Question 19

Test: Coordinate Geometry- 2 - Question 20

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?

Detailed Solution for Test: Coordinate Geometry- 2 - Question 20

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