Suppose a triangle is formed by x+y=10 and th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The triangle is formed by the lines $x=0$,$y=0$,and $x+y=10$. The vertices are $O(0,0)$,$A(10,0)$,and $B(0,10)$.We need to find the number of poin

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(A) The triangle is formed by the lines $x=0$,$y=0$,and $x+y=10$. The vertices are $O(0,0)$,$A(10,0)$,and $B(0,10)$.We need to find the number of points $(x, y)$ such that $x, y \in \mathbb{N}$ (natural numbers) and $x+y If $x=1$,then $1+y If $x=2$,then $2+y Continuing this pattern,for a given $x$,the number of natural number values for $y$ is $9-x$.Since $x$ must be a natural number,$x$ can range from $1$ to $8$ (because if $x=9$,$y The total number of points is the sum: $8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = \frac{8 	imes 9}{2} = 36$.

Suppose a triangle is formed by $x+y=10$ and the coordinate axes. Then the number of points $(x, y)$ where $x$ and $y$ are natural numbers,lying inside the triangle is

Similar Questions

The area of the triangle formed by the line $x \sin \alpha + y \cos \alpha = \sin 2\alpha$ and the coordinate axes is

If the incentre and the circumcentre of the triangle formed by the lines $x=2$,$4x+3y+7=0$ and $y=3$ are $I$ and $S$ respectively,then $IS=$

The equations of the sides of a triangle are $x - 3y = 0$,$4x + 3y = 5$,and $3x + y = 0$. The line $3x - 4y = 0$ passes through:

What is the ratio of the area of $\triangle PQS$ to the area of $\triangle PQR$?

Straight lines $x-y=7$ and $x+4y=2$ intersect at $B$. Points $A$ and $C$ are so chosen on these two lines such that $AB=AC$. The equation of line $AC$ passing through $(2,-7)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module