M L Aggarwal Solutions for Chapter: Straight Lines, Exercise 4: EXERCISE

Find the value of $y$ so that the line through $(3, y)$ and $(2,7)$ is parallel to the line through $(-1,4)$ and $(0,6) ?$

Find the value of $x$ so that the points $(6,-1),(5,0) \mathrm{and} (x, 3)$ are collinear.

Find the value of $x$ so that the points $(6,-1),(5,0) \mathrm{and} (x, 3)$ are collinear.

If $A(2,-3)$ and$B(3,5)$ are two vertices of a rectangle $ABCD$, find the slope of $CD$.

If $\mathrm{A}(2,-3)$ and $\mathrm{B}(3,5)$ are two vertices of a rectangle $\mathrm{ABCD}$, find the slope of $\mathrm{DA}$.

Using slopes, prove that the points $(-4,-1),(-2,-4),(4,0)$ and $(2,3)$, taken in order, are the vertices of a rectangle.

The vertices of a quadrilateral are $(-4,2),(2,6),(8,5) \mathrm{and} (9,-7)$. Using slopes, show that the midpoints of the sides of the quadrilateral form a parallelogram.

If the points $A\left(x_1,y_1\right),B\left(x_2,y_2\right)$and $P\left(h,k\right)$ are collinear, prove that $\left(h-x_1\right)\left(y_2-y_1\right)=\left(k-y_1\right)\left(x_2-x_1\right)$.