Distance between Points Lying Parallel to X & Y Coordinates

Q. The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are

(a) (3, 0)

(b) (0, 2)

(c) (2, 3)

(d) (3, 2)

Q.

Find the area of triangle formed by the points A(5, 2), B(4, 7) and C(7, -4).

__ square units

Q.

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs the distance AD on the 2^nd line and posts a green flag. Preet runs the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

Q.

The points $(1,3)$ and $(5,1)$ are the opposite vertices of a rectangle. The other two vertices lie on the line $y=2x+c$, then the value of $c$ will be

1. $4$

2. $-4$

3. $2$

4. $-2$

Q. The distance of the point P(2, 3) from the x-axis is

1. $5$
2. $3$
3. $2$
4. $1$

Q. What will be the difference between the abscissa of point A and point B?

1. 3
2. 6
3. 1
4. 0

Q. If the coordinates of A and B respectively are (-4, 3) and (8, -6), then
(i) find the length of AB.
(ii) In what ratio, is the line joining AB divided by the x-axis?
[4 MARKS]

Q. 99. if (2, 1) (4, 5) (-1, -3) are the mid points of the sides of triangle then the coordinate pf its vertices are

Q.

Prove that the diagonals of a rectangle bisect each other and are equal.

Q.

A line intersects the y axis and x axis at the points P and Q respectively.If (2, -5) is the mid point of PQ, then find the cordinates of P and Q.

Q.

The coordinates of some pairs of points are given below. Without drawing the axes of coordinates, mark these points with the left-right, up-down positions correct. Draw rectangle with these as opposite vertices. Find the coordinates of the other two vertices and the lengths of the sides of these rectangles:

(i) (3, 5), (7, 8)

(ii) (−3, 5), (−7, 1)

(iii) (6, 2), (5, 4)

(iv) (−1, −2), (−5, −4)

Q.

If the coordinates of a triangle are A(2, 1), B(6, 1), C(6, 5) then find the length of BC.

1. 3 units

2. 4 units

3. -4 units

4. -3 units

Q. P is a point on the cartesian plane. P' is its refection over positive x axis. Find the distance between these two points.

1. 6
2. 3
3. 9
4. 0

Q.

In the figure below, is any side of ΔABC parallel to X-axis? If so, the side is:

1. AC

2. AB

3. none of these

4. BC

Q.

If the coordinates of a triangle ABC is A(3, 1), B(5, 1) and C(6, 8) then find the side of the triangle which is parallel to the X-axis.

1. CA

2. BC

3. AB

4. All of the above

Q. The line $ax+by=ab$, will meet the y- axis at _____.

1. $(0,a)$
2. $(a,0)$
3. $(0,b)$
4. $(b,0)$

Q. Find the distance between two points A(-3, 2) and B(-3, -3).

1. 4 units and parallel to X-Axis
2. 5 units and parallel to Y-Axis
3. 4 units and parallel to X-axis
4. 5 units and perpendicular to X-axis

Q.

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'Q' is ___

1. (10, -4)

2. (-4, 10)

3. (4, 10)

4. (10, 4)

Q. A line intersects the y-axis and x-axis at P and Q , respectively. If (2, $-$5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
(a) (0, $-$5) and (2, 0) (b) (0, 10) and ($-$4, 0)
(c) (0, 4) and ($-$10, 0 ) (d) (0, $-$10) and (4 , 0)

Q.

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'P' is ___

1. (-2, -4)

2. (2, -4)

3. (-2, 4)

4. (4, 2)

Q.

Find the point equidistant from the points P(1, 3) and Q(-5, -5), and which lies on the line $y=-1$.

1. (-2, -1)

2. (-4, -1)

3. (3, -1)

4. (-2, -2)

Q.

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'S' are ___

1. (2, 0)

2. (0, -2)

3. (2, 2)

4. (-2, 0)

Q.

In the point $(4,7),4$ denotes the __________.

Q.

Points $P(1,3)$ and $Q(-5,-5)$ are two points in the coordinate plane. The X-coordinate of the point equidistant from the points $P$ and $Q$ and lying on the line $y=-1$ is

___

Q. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, −5) is the midpoint of PQ, then the coordinates of P and Q, respectively, are

(a) (0, −5) and (2, 0)
(b) (0, −10) and (4, 0)
(c) (0, 10) and (−4, 0)
(d) (0, 4) and (−10, 0)

Q.

If the coordinates of a triangle ABC is A(3, 1), B(5, 1) and C(5, 8) then find the side of the triangle which is parallel to the Y-axis.

1. BC

2. AB

3. All of the above

4. CA

Q.

The slope of the line that is parallel to x – axis is _____.

1. 1

2. Not definite

3. Insufficient data

4. 0

Q.

What is the x coordinate of point C?

__

Q.

Find the area of triangle formed by the points A(5, 2) B (4, 7) and C (7, -4).

__

Q.

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'C' is ___

1. (3, 0)

2. (3, -4)

3. (3, -8)

4. (3, -10)