Assessment 1 - Coordinate Geometry - Ix

The point (2,1) lies to the right of the Y-axis because the X-coordinate is positive. In a Cartesian coordinate system, the Y-axis is the vertical line that divides the plane into two halves. The positive X-axis is to the right of the Y-axis, and the negative X-axis is to the left. Since the X-coordinate of (2,1) is positive, it is to the right of the Y-axis.

The given points form a square because all sides are equal in length and all angles are right angles. A square is a type of quadrilateral where all sides are equal and all angles are right angles.

The point R (-3, -8) is the only point in the third quadrant. The third quadrant is defined as the area where both the x-coordinate and y-coordinate are negative. In this case, both the x-coordinate (-3) and y-coordinate (-8) of point R are negative, placing it in the third quadrant. Therefore, the correct answer is R only.

The point (x+y, u+v) can be calculated as (3+2, 9+(-13)) which equals (5, -4). In the coordinate plane, the positive x-axis is to the right and the positive y-axis is upwards. Since the x-coordinate is positive and the y-coordinate is negative, the point lies in the IV quadrant.

If the x-coordinate of a point is zero, it means that the point lies on the y-axis. This is because the y-axis is the vertical line where the x-coordinate is always zero. Therefore, any point with a zero x-coordinate will lie on the y-axis.

The correct answer is (-2,4) because it is the only option that matches the given coordinates. The coordinates of P are (-2,4) as indicated in the figure.

The point at which the two coordinate axes meet is called the origin. This is the starting point or reference point for measuring distances on a coordinate plane. It is represented by the coordinates (0,0) and is where the x-axis and y-axis intersect.

The y-coordinate of a point represents its distance from the x-axis. Since the foot of the perpendicular lies on the negative direction of the x-axis, the point P can have a y-coordinate of either 7 or -7.

The coordinates of any point on the y-axis are of the form (0, k), where |k| is the distance of the point from the x-axis. This is because the y-axis is a vertical line that passes through the origin, and the x-coordinate of any point on the y-axis is always 0. Therefore, the distance of any point on the y-axis from the x-axis is measured along the x-axis, which is the x-axis itself.

All angles in a triangle add up to 180 degrees.