Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
If the points
If
and
be three points such that area of a
is 4 sq units, find the value of
.
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Find the value of
for which the area of a ABC having vertices
and
is 35 sq units.
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Find the value of
for which the points
and
are collinear.
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Find the value of
for which the points
and
are collinear.
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Find the value of
for which the points
and
are collinear.
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Use determinants to show that the following points are collinear.
and ![Rendered by QuickLaTeX.com R(-5,-4)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fd5c78358e54f7c2902030112f53c513_l3.png)
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Use determinants to show that the following points are collinear.
and ![Rendered by QuickLaTeX.com C(10,14)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5deb6e4c4e20f7e78f807dbbc34aabf2_l3.png)
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Use determinants to show that the following points are collinear.
and ![Rendered by QuickLaTeX.com C(5,8)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-cc1ec3609415d61387386f89725dd44a_l3.png)
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Find the area of the triangle whose vertices are:
and ![Rendered by QuickLaTeX.com R(10,8)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1aaf401ff2b3d4bb3b5d0a8f2ef9798b_l3.png)
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Find the area of the triangle whose vertices are:
and ![Rendered by QuickLaTeX.com R(4,3)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3c4c4861ffeb040f077ac94b42a82d08_l3.png)
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Find the area of the triangle whose vertices are:
and ![Rendered by QuickLaTeX.com C(-1,5)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-add32e746e0d76d57e8a4d88a682c9d2_l3.png)
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Find the area of the triangle whose vertices are:
and ![Rendered by QuickLaTeX.com C(5,4)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a4a4e665b78e9579adc8f25aa4cf14bc_l3.png)
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
Find the area of the triangle whose vertices are:
and ![Rendered by QuickLaTeX.com C(5,-1)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-09023f26dd604aea3dbcea1fefb32ccd_l3.png)
Solution: Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3}...
A girl goes to her friend’s house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining distance at a speed of (x + 2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance, find ‘x’.
Given, The young lady covers a distance of 6 km at a speed x km/hr. Along these lines, the time taken to cover initial 6 km \[=\text{ }6/x\text{ }hr\] [Since, Time = Distance/Speed] Likewise given,...
A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.
We should accept x km/h to be the first speed of the vehicle. We realize that, Time = Distance/Speed From the inquiry, The time taken by the vehicle to finish 400 km = \[400/x\text{ }hrs\]...
If the speed of an aeroplane is reduced by 40 km/hr, it takes 20 minutes more to cover 1200 km. Find the speed of the aeroplane.
How about we think about the first speed of the plane to be x km/hr. Presently, the time taken to cover a distance of \[1200\text{ }km\text{ }=\text{ }1200/x\text{ }hrs\] [Since, Time =...
The speed of an ordinary train is x km per hr and that of an express train is (x + 25) km per hr. (i) Find the time taken by each train to cover 300 km. (ii) If the ordinary train takes 2 hrs more than the express train; calculate speed of the express train.
(i) Given, Speed of the conventional train \[=\text{ }x\text{ }km/hr\] Speed of the express train \[=\text{ }\left( x\text{ }+\text{ }25 \right)\text{ }km/hr\] Distance \[=\text{ }300\text{ }km\] We...