Geometry

Miscellaneous

Medium

If the distance between the points (2, -2) and (5, k) is 5 units, then one of the possible values of k shall be which of the following?

✅ Correct Option: 3

The distance between points (2, -2) and (5, k) is 5 units.

Using the distance formula:

$\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$5 = \sqrt{(5 - 2)^2 + (k - (-2))^2}$

$5 = \sqrt{(3)^2 + (k + 2)^2}$

$5 = \sqrt{9 + (k + 2)^2}$

Squaring both sides:

$25 = 9 + (k + 2)^2$

$(k + 2)^2 = 16$

Taking the square root of both sides:

$k + 2 = \pm 4$

This gives two possible values:

$k + 2 = 4$

$k = 2$

$k + 2 = -4$

$k = -6$

The possible values of k are 2 and -6.

Therefore, one of the possible values of k is 2.

2026: 19 May Shift 2

Find the coordinates of the point which divides the line segment joining the points (4,-1) and (-2,-3) in the ratio 2 : 3 internally.

2026: 31 May Shift 2

The point (x, y) is equidistant from the points (2, 4) and (1, 8). Find the relation between x and y.

2026: 24 May Shift 1

Match List-I with List-II

List-I (Statements, etc.)	List-II (Values, etc.)
(A) Coordinates of origin	(I) (0, y)
(B) Distance of a point from itself	(II) (x, 0)
(C) Any point on the y axis	(III) (0, 0)
(D) Any point on the x axis	(IV) 0

Choose the correct answer from the options given below:

2025: 19 May Shift 2

If two vertices of a triangle are (5, 4) and (-2, 4) and centroid is (5,6), then third vertex is:

2026: 30 May Shift 1

To locate the position of an object or a point in a plane, we require the following perpendicular lines.

2023: 19 June Shift 1

Match List - I with List - II.

Choose the correct answer from the options given below :

Solution