Question

Aadya and Nitya planted so.e trees in a square garden. Aadya plant the trees on the points A1(2,1),A2(4,3) and A3(6,5) and Nitya planted th etrees on the points N1(2,3),N2(3,4) and N3(4,6). Both arguing that they have planted trees in a straight line. Find out who is correct. Justify your answer.

Answer 1

Aadya has planted in a straight line.

Step-by-step explanation:

If the three points are on a straight line or co-linear, slopes between them will be same.

Since Aadya has planted trees at $A_{1}(2, 1),A_{2}(4,3),A_{3}(6,5)$. If these points are co-linear slopes joining the points will be same.

Slope of line segment $A_{1} A_{2}$ = $\frac{y-y'}{x-x'}=\frac{3-1}{4-2}$ =1

Now slope of $A_{2} A_{3}$ = $\frac{y"-y'}{x"-x'}=\frac{5-3}{6-4}=1$

Therefore, all three points are co-linear.

Similarly Nitya planted the trees at $N_{1}(2,3), N_{2}(3,4),N_{3}(4,6)$.

slope of $N_{1} N_{2}=\frac{4-3}{3-2}=1$

Slope of  $N_{2} N_{3}=\frac{6-4}{4-3}=2$

Here the slopes of segments $N_{2} N_{3}$ and $N_{1} N_{2}$ are different which conclude that these points are non co-linear.

Therefore, Aadya is correct.

Learn more to find slopes from :https://brainly.in/question/5280445