H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Co-Ordinate Geometry, Exercise 4: EXERCISE

Find the area of the quadrilateral whose vertices are:

$(1, 1), (3, 4), (5, -2)$ and $(4, -7)$

If the area of a quadrilateral, whose vertices are $A, B, C, D,$ taken in order, are $(1, 2), (-5, 6), (7, -4)$ and $(k, -2)$ be zero, find the value of $k$.

If the area of the triangle formed by the following points is $k^2 \mathrm{sq}. \mathrm{unit}$ then find $k$.

$(a, c+a), (a, c)$ and $(-a, c-a)$

If the length of the altitude of the triangle is$\frac{24}{\sqrt{k}}$ , coordinates of whose vertices are $(5, 1), (2, 4)$ and $(-1, -1)$.

Find the value of $k$.

$A, B$ are the two points $(3, 4)$ and $(5, -2)$ . Find the point $P$ such that $PA=PB$ and the area of $∆PAB$ is equal to $10$.

$A, B, C$ are the points $(-1, 5), (3, 1)$ and $(5, 7)$ and $D, E, F$ are the midpoints of $BC, CA$ and $AB$ respectively. Prove that $∆ABC$ is equal to four times of area of $∆DEF$.

For what value of $x$ will the points $(x, 3), (-5, 6)$ and $(-8, 8)$ be collinear. Express your answer as a rational number.

Prove that the three points $(3a, 0), (0, 3b)$ and $(a, 2b)$ are collinear.