Locating a Point in Cartesian Plane

Q.

Find the value of a and b

5+✓3/7-4✓3=a+✓3b

Q.

If the points A (6, 1), B (8, 2), C (9, 4) and D (p, 3) are vertices of a parallelogram, taken in order, find the value of p

Q. If a+b+c= 6 and 1/a + 1/b + 1/c = 3/2, then find a/b + a/c + b/a + b/c + c/a + c/b. Kindly show the detailed steps.

Q. The distance of a point from the Y-axis is called _____.

1. Y-coordinate
2. abscissa
3. ordinate
4. (a) and (b) above.

Q.

Write the coordinates of a point which lies on the y-axis and is at a distance of y units below the x-axis.

Q.

The abscissa or x-coordinate of any point on Y-axis is:

1. Zero

2. Two

3. Three

4. One

Q.

The abscissa of any point on Y-axis is:

1. Three

2. One

3. Zero

4. Two

Q. Find the joint equation of the pair of lines through the origin , one of which is parallel to 2x+y=5 and other is perpendicular to 3x-4x+7=0.

Q.

If f(x) =2x - 1 , what is f(-5)

Q.

If x and y take only natural number values, find the number of (x, y) pairs satisfying the equation 2x+5y=100

Q.

If a + b = 5 and a - b = 1 find the value of a² + b²/2ab

Q. A point whose abscissa is −3 and ordinate 2 lies in

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

Q.

Given that If x is not equal to y , the (x, y) is not equal to (y, x) But if x = y , the (x, y ) = ( y, x)

1. True

2. False

Q.

Factorise:

$9a^2-4b^2-6a+1$

Q. The equation of a line through the intersection of lines x = 0 and y = 0 and through the point (2, 2), is

1. y = x – 1
2. y = –x
3. y = x
4. y = –x + 2

Q.

If cot theta = - 3/4 and theta is not in the 2nd quadrant then 5 sin theta + 10 cos theta + 9 sec theta + 16cosec theta - 4 cot theta =

Q.

In which quadrant or on which axis do each of the points and lie? Verify your answer by locating them on the Cartesian plane.

Q.

State true or false. The point (2, 0) lies in both the $1^{st}$ and $4^{th}$ quadrants.

1. True

2. False

Q.

Question 2 (iv)
Write the point identified by the coordinates (2, -4).

Q.

If 2x + 3y = 12 and xy = 5, find the value of 4x² + 9y².

1. 98

2. 67

3. 84

4. 56

Q.

Signs of abscissa and ordinate of a point in the third quadrant will be-

1. -, -

2. -, +

3. +, -

4. +, +

Q. If $x=\left(4-\sqrt{15}\right)$, find the value of $\left(x+\frac{1}{x}\right)$.

Q.

Describe the translation of the point to its image.
$(3,-2)\to (1,0)$

Q. The point (5, -6) lies in the .

1. 1st Quadrant
2. 4th Quadrant
3. 3rd Quadrant

Q. If 10^2y = 25, then 10^-y equals

(a) $-\frac{1}{5}$

(b) $\frac{1}{50}$

(c) $\frac{1}{625}$

(d) $\frac{1}{5}$

Q. The abscissa and ordinate of the origin are

(a) (0, 0)

(b) (1, 0)

(c) (0, 1)

(d) (1, 1)

Q.

M (-2, y) is a point equidistant from the coordinates A(5, 7) and B(3, -4). Find the value of y.

1. 2
2. 
3. 

4. 

Q.

5x-9=1/y

X+1/y=3

Q. Without plotting the points on a graph paper indicate the quadrant in which they lie:
(i) ordinate = 4, abscissa = −3
(ii) ordinate = −5, abscissa = 4
(iii) abscissa = −1, ordinate = −2
(iv) abscissa = −5, ordinate = 3
(v) abscissa = 2, ordinate = 1
(vi) abscissa = 7, ordinate = −4

Q. If a < 0 and b < 0, then the point P(a, b) lies in
(a) quadrant IV
(b) quadrant II
(c) quadrant III
(d) quadrant I