Distance between Two Points on the Same Coordinate Axes

Q.

The point on Y-axis equidistant from (–3, 4) and (7, 6) is ___.

1. (0, 15)

2. (0, 14)

3. (0, 13)

4. (15 , 0)

Q. The point $(2,3)$ is at a distance of _________ units from X-axis

1. $2$ units
2. $5$units
3. $3$ units
4. None of these

Q.

Find the distance between the points
(i) P(-6, 7) and Q(-1, -5)
(ii) R(a + b, a - b) and S(a - b, - a - b)

Q.

A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $\Delta ABC$, if AB and BC are parallel to the coordinate axes as shown in the figure.

1. 12 sq. units

2. 10 sq. units

3. 6 sq. units

4. 20 sq. units

Q. Find the point on the y-axis which is equidistant from A (3, - 4) and B (- 5, 9). $\left[3\text{Marks}\right]$

Q.

Area of square ABCD with A(1, 0) and B(4, 0) is ___ square units.

Q.

The point on the X-axis which is equidistant from point A(4, 6) and B(-1, 3) is

1. $(4.5,0)$

2. $(1.5,4.5)$

3. $(4.2,0)$

4. $(1.5,0)$

Q.

Match the two columns.
$\begin{array}{cc}Column-I& Column-II\\ \left(A\right)Thedistanceofapointfromthex-axisarecalled& \left(p\right)Coordinateaxes\\ \left(B\right)Thedistanceofapointfromthey-axisarecalled& \left(q\right)Ordinate\\ \left(C\right)Thelinesofacoordinateplanearecalled& \left(r\right)quadrants\\ \left(D\right)Thepartsofaplanemadebythecoordinateaxesarecalled& \left(s\right)abscissa\end{array}$
Choose the correct option:

1. $\left(A\right)\to s;\left(B\right)\to q;\left(C\right)\to p;\left(D\right)\to r$

2. $\left(A\right)\to q;\left(B\right)\to s;\left(C\right)\to r;\left(D\right)\to p$

3. $\left(A\right)\to s;\left(B\right)\to q;\left(C\right)\to r;\left(D\right)\to p$

4. $\left(A\right)\to q;\left(B\right)\to s;\left(C\right)\to p;\left(D\right)\to r$

Q. If diagonals of a parallelogram are equal then show that it is a rectangle with diagrams

Q. In the graph alongside, line LM is parallel to the Y-axis.

1. What is the distance of line LM from the Y-axis?
2. Write the co-ordinates of the points P, Q and R.

Q. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Q. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Q. Find the values of y for which the distance between the points P (2, - 3) and Q (10, y) is 10 units.

Q. The point $(1,\beta )$ lies on or inside the triangle formed by the lines y = x, x - axis and x + y =8

Q.

If the distance between points P (x, 2) and Q (3, –­6) is 10 units, then x is

1. 3

2. -3

3. 9

4. -9

Q.

The number of points on x-axis which are at a distance $c(c<3)$ from the points (2, 3) is

1. 2

2. 1

3. Infinite

4. None of these

Q.

In the given graph, the sum of the x co-ordinate and y co-ordinate of the point is _____ .

1. 4
2. 5
3. 3

4. 2

Q. In the graph alongside, line LM is parallel to the Y-axis.

1. What is the distance of line LM from the Y-axis?
2. Write the co-ordinates of the points P, Q and R.

Q.

Draw the graph of 𝒚 = 𝒙 + 𝟑 and find the coordinates of the points of intersection with the axes.

Q. P is the point on the y-axis which is equidistant from A(-5, -2) and B(3, 2), then PA = ___ cm.

1. 3
2. 5
3. 2
4. 6

Q.

What is the distance of the point (6, 18) from the X-axis?

1. 18

2. 6

3. 4

4. 10

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