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Introduction To Euclid's Geometry

Question

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Draw the graph of the equations x = 3 and 4x = 3y in the same graph. Find the area of the triangle formed by these two lines and the x-axis.

Solution

x = 3 represents a line parallel to y-axis at a distance of 3 units to the right of the origin.
4x = 3y

rightwards double arrow space

straight y space equals fraction numerator 4 straight x over denominator 3 end fraction

Table of solutions

x	0	3
y	0	4

We plot the points (0, 0) and (3, 4) on a graph paper and join the same by a ruler to get the line which is the graph of the equation 4x = 3y.

Area of the triangle OAB formed by the given two lines and the x-axis

equals fraction numerator 3 cross times 4 over denominator 2 end fraction equals 6

square units.

Some More Questions From Introduction to Euclid's Geometry Chapter

Express the following statement as a linear equation in two variables by taking present ages (in years) of father and son as x and y, respectively. Age of father 5 years ago was two years more than 7 times the age of his son at that time.

Write the equation 2x = y in the form ax + by + c = 0 and find the values of a, b, c in the equation. How many solution this equation has?

Express the linear equation 7 = 2x in the form ax + by + c = 0 and also write the values of a, b and c

Write each of the following as an equation in two variables:

(i) x = – 5 (ii) y = 2

(iii) 2x = 3 (iv) 5y = 2.

Which one of the following options is true, and why?

y = 3x + 5 has

(i) a unique solution,
(ii) only two solutions,
(iii) infinitely many solutions.

Write four solutions for each of the following equations:

2x + y = 7

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