Write whether the following statements are True or False. Justify your answer.

By Ritesh|Updated : November 15th, 2022

(i) Point (3, 0) lies in the first quadrant.

(ii) Points (1, -1) and (-1, 1) lie in the same quadrant.

(iii) The coordinates of a point whose ordinate is - 1/2 and abscissa are 1 are - 1/2, 1.

(iv) A point lies on the y-axis at a distance of 2 units from the x-axis. Its coordinates are (2, 0). (v) (-1, 7) is a point in the II quadrant.

Solution:

(i) Point (3, 0) lies in the first quadrant.

The following assertion is untrue.

Points with x-coordinates of "0" are located on the Y axis, while points with y-coordinates of "0" are located on the X axis.

The coordinates (3, 0) have a zero ordinate.

The point is therefore on the x-axis.

(ii) Points (1, –1) and (–1, 1) lie in the same quadrant.

The following assertion is untrue.

The following is a representation of the coordinates of points in the quadrants:

Quadrant 1 : (+x, +y)

Quadrant 2 : (-x, +y)

Quadrant 3 : (-x, -y)

Quadrant 4 : (+x, -y)

(1, -1) lies in the IV quadrant

(-1, 1) lies in the II quadrant.

(iii) The coordinates of a point whose ordinate is – ½ and abscissa are 1 are – 1/2, 1.

The following assertion is False

The form of the cartesian coordinates is (x, y). The abscissa and ordinate are the names for the ordered pairings in the two-dimensional plane.

The ordered pair's first number is referred to as the abcissa. In other words, the abscissa is the value of x in the ordered pair. It is any point on the plane's separation from the y-axis.

Ordinate: The ordinate is the second number in the ordered pair. It uses y's value. Any point on the plane's ordinate is measured in relation to the x-axis.

The coordinates of a point whose ordinate is – ½ and abscissa are 1 are (1, -1/2).

(iv) A point on the y-axis is located two units away from the x-axis. Its location is at (2, 0).

The following assertion is untrue.

A point on the y-axis is located two units away from the x-axis. Its location is at (0, 2).

(–1, 7) is a point in the II quadrant.

The provided statement is accurate Justification:

The following is a representation of the coordinates of points in the quadrants:

Quadrant 1 : (+x, +y)

Quadrant 2 : (-x, +y)

Quadrant 3 : (-x, -y)

Quadrant 4 : (+x, -y)

(–1, 7) is a point in the II quadrant.

Summary:

Write whether the following statements are True or False. Justify your answer. (i) Point (3, 0) lies in the first quadrant. (ii) Points (1, -1) and (-1, 1) lie in the same quadrant. (iii) The coordinates of a point whose ordinate is - 1/2 and abscissa are 1 are - 1/2, 1. (iv) A point lies on y-axis at a distance of 2 units from the x-axis. Its coordinates are (2, 0). (v) (-1, 7) is a point in the II quadrant.

The statements:

(i) Point (3, 0) lies in the first quadrant and is false

(ii) Points (1, -1) and (-1, 1) lie in the same quadrant is false

(iii) The coordinates of a point whose ordinate is - 1/2 and abscissa are 1 are - 1/2, 1 is false.

(iv) A point lies on the y-axis at a distance of 2 units from the x-axis. Its coordinates are (2, 0) is false

(v) (-1, 7) is a point in the II quadrant that is true.

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