Question

A friend of Steve who is a gardener is dealing with some issues about planting seeds. It turns out that she has a square garden and decided to plant seeds of beautiful flowering plants at these following particular locations. Now, she decided to plant a seed at a location E which is given by $(0,5)$. Will E lie on the same line segment joing AB?

• A. Yes
• B. No
• C. Data Insufficient

Answer 1

The correct option is A Yes

The coordinates of $A$ and $B$ are $(3,5)$ and $(-5,5)$, respectively. Now, the question is: does the point $E=(0,5)$ land in-between the line segment $AB$ ?


The $y$-coordinate of both $A$ and $B$ is 5, which means $AB$ lies on the horizontal line of $y=5$.


As the $y$-coordinate of the point $E$ is also 5, its for sure, $E$ will lie on the line joining the points $A$ and $B$, but may or may not lie on the line segment $AB$.

The $x$-coordinate of $B$ is $-5$ and the $x$-coordinate of $A$ is $3$. Hence, the $x$-coordinate of $E$, which is $0$, lies in-between $-5$ and $3$ as $-5<0<3$.


$\therefore$ Yes, the point $E$ will lie on the line segment joining $AB$.