Question

Find the equation of a line passing through the point A(1,4) and
perpendicular to the line joining points (2,5) and (4,7).

Answer 1

Given,

Point A = (1,4)

Line joining points (2,5) and (4,7).

To find,

The equation of a line passing through A(1,4) and perpendicular to the line connecting points (2,5) and (4,7).

Solution,

We may use the following mathematical procedure to solve the issue.

The following is the procedure for determining the equation of the line.

We know that,

The equation of a straight line by two-point form is:

⇒ (y- y₁) = $\frac{y2-y1}{x2-x1}$(x - x₁),

where (x₁,y₁) and (x₂,y₂) are two points.

∴ The slope of the line = $\frac{y2-y1}{x2-x1}$

                                      = $\frac{7-5}{4-2}$

                                      = 1

We know that,

Product of slopes of perpendicular lines = -1

Thus,

The slope of the perpendicular line = -1

By slope-point form,

⇒ (y - y₁) = m(x-x₁)

⇒ (y - 4) = -1 (x -1)

⇒ y - 4 = 1 - x

⇒ y + x = 5

As a result, the equation of a line passing through A(1,4) and perpendicular to the line connecting points (2,5) and (4,7). is y + x = 5.