Q. 44.3( 3 Votes )

# Fill in the blanks:

(a) The y-coordinate of a point on the x-axis is _________.

b) The x-coordinate is called as _________.

(c) The x-axis and Y-axis intersect at _________.

(d) If a point (x,y) ≠ (0,0) is in the third quadrant, then x + y has _________sign.

(e) If a point (x,y) lies above horizontal axis, then y is always _________.

(f) The point of intersection of x = y and x = −y is _________.

(g) The line y =4x +5 intersects y-axis at the point _________.

Answer :

(a) The y-coordinate of a point on the x-axis is **zero.**

Explanation:

On x – axis, the values of x keep on increasing and value of y remains zero as there is no movement in vertical direction.

(b) The x-coordinate is called as **abscissa**.

Explanation: The x coordinate of a coordinate system is called abscissa and y coordinate is called ordinate.

(c) The x-axis and Y-axis intersect at **origin (0,0).**

At origin values of x and y coordinates are 0 and thus they start increasing or decreasing in value from origin. Thus, they intersect at origin.

(d) If a point (x,y) ≠ (0,0) is in the third quadrant, then x + y has **–(negative)** sign.

Explanation: In the third quadrant, x and y both are negative, thus x – y = -x + (-y) = - (x + y)

And so its negative.

(e) If a point (x,y) lies above horizontal axis, then y is always **+(positive).**

(As, in first and second quadrant y is positive.)

(f) The point of intersection of x = y and x = −y is **origin(0,0)**.

(As, after solving both the equations simultaneously by using substitution method, we get- x=0 and y=0).

(g) The line y =4x +5 intersects y-axis at the point **(0, 5)**.

(Since, the point is at y-axis implies that x=0, and after substituting x=0 in equation, we get y=5.

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Suppose P has coordinates (10,2) in a coordinate system X ’OX−Y ’OY and (−3,−6) in another coordinate system X_{1}’O_{1}X_{1}↔ Y_{1}’O_{1}Y_{1}? with X ’OX ║ X_{1}’O_{1}X_{1}. Determine the coordinates of O with respect to the system X_{1}’O_{1}X_{1}↔ Y_{1}’O_{1}Y_{1}.

Suppose you are given a coordinate system. Determine the quadrant in which the following points lie:

(i) A (4,5) (ii) B (−4,−5) (iii) C (4,−5).

Karnataka Board - Mathematics Part IIA point P has coordinates (7,10) in a coordinate system X′OX ↔ Y′OY. Suppose it has coordinates (10,7) in another coordinate system X′_{1}O_{1}X_{1}↔ Y′_{1}O_{1}Y_{1} with X′OX || X′_{1}O_{1}X_{1}. Find the coordinates of O_{1} in the system X′OX ↔ Y′OY.

Match the following:

Karnataka Board - Mathematics Part II

Suppose P is a point with coordinates (−8,3) with respect to a coordinate system X’OX ↔ Y’OY. Let X_{1}’O_{1}X_{1}↔ Y_{1}’O_{1}Y_{1} be another system with X’OX ║X_{1}’O_{1}X_{1} and suppose O_{1} has coordinates (9,5) with respect to X ’OX ↔ Y ’OY. What are the coordinates of P in the system X_{1}’O_{1}X_{1}↔ Y_{1} ’O_{1}Y_{1}?