Question

write the coordinates of another point on the line passing through the points A(2,1),B(7,1)

Answer 1

Answer:

The points on the line AB are in the form of (x,1). Where, x can be any real number.

Step-by-step explanation:

The line passing through the points A(2,1) and B(7,1).

If a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of line AB is

$y-1=\frac{1-1}{7-2}(x-2)$

$y-1=0(x-2)$

$y-1=0$

$y=1$

The equation of line is y=1, it means the value of y-coordinate is always 1 and the points on the line AB are in the form of (x,1). Where, x can be any real number.

Answer 2

Answer: (5,1).

Step-by-step explanation: Given points are A(2,1) and B(7,1). To find any other point on the line joining A and B, we need to first find the equation of the line AB.

Slope of line AB is given by

$m=\dfrac{1-1}{7-2}=\dfrac{0}{5}=0.$

So, the equation of the line AB is

$y-1=m(x-2)\\\Rightarrowy-1=0(x-2)\\\Rightarrow y=1.$

Hence, another point on the line AB is (5,1), (3,1), (-4,1), etc.