Question 1

What is the distance of the point P(3, 4) from the origin?

Accepted Answer

The distance of a point P(x, y) from the origin is given by the formula $\sqrt{x^2 + y^2}$. Substituting the given coordinates x = 3 and y = 4, we get $\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$ units. Therefore, the correct option is B.

Question 2

The distance between the points (2, 3) and (4, 1) is:

Accepted Answer

Using the distance formula $\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$, we substitute $(x1, y1) = (2, 3)$ and $(x2, y2) = (4, 1)$. This gives $\sqrt{(4 - 2)^2 + (1 - 3)^2} = \sqrt{(2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$ units. Therefore, the correct option is C.

Question 3

The coordinates of the midpoint of the line segment joining the points (1, 2) and (3, 4) are:

Accepted Answer

The midpoint formula is given by $\left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)$. Substituting the coordinates $(1, 2)$ and $(3, 4)$, we get $\left(\frac{1 + 3}{2}, \frac{2 + 4}{2}\right) = \left(\frac{4}{2}, \frac{6}{2}\right) = (2, 3)$. Therefore, the correct option is A.

Question 4

The centroid of a triangle whose vertices are $(x1, y1)$, $(x2, y2)$ and $(x3, y3)$ is given by:

Accepted Answer

The formula for the centroid of a triangle with vertices $(x1, y1)$, $(x2, y2)$, and $(x3, y3)$ is $\left(\frac{x1 + x2 + x3}{3}, \frac{y1 + y2 + y3}{3}\right)$. Therefore, the correct option is D.

Question 5

The point which divides the line segment joining the points $(4, -3)$ and $(8, 5)$ in the ratio $3:1$ internally is:

Accepted Answer

Using the section formula $\left(\frac{m1x2 + m2x1}{m1 + m2}, \frac{m1y2 + m2y1}{m1 + m2}\right)$, with $m1=3, m2=1, x1=4, y1=-3, x2=8, y2=5$, we get $\left(\frac{3(8) + 1(4)}{3 + 1}, \frac{3(5) + 1(-3)}{3 + 1}\right) = \left(\frac{24 + 4}{4}, \frac{15 - 3}{4}\right) = \left(\frac{28}{4}, \frac{12}{

Coordinate Geometry