# Video: Pack 1 β’ Paper 1 β’ Question 18

Pack 1 β’ Paper 1 β’ Question 18

02:04

### Video Transcript

In the diagram, π΄π΅πΆπ· is a square. The equation of the side π΄π΅ is π¦ equals one-third π₯ plus five and the coordinates of point π΄ are three, six. Work out the equation of the side π΄π·.

As the equation π¦ equals one-third π₯ plus five is in the form π¦ equals ππ₯ plus π, its gradient must be one-third. As π΄π΅πΆπ· is a square, the lines π΄π΅ and π΄π· are perpendicular. If two lines are perpendicular, the product of their gradients is equal to minus one: π one multiplied by π two is equal to minus one.

In this case, one-third multiplied by π two is equal to minus one. Multiplying both sides of this equation by three gives us π two is equal to minus three. Therefore, the gradient of π΄π· is minus three. As the gradient is equal to minus three, the equation of π΄π· must be π¦ equals minus three π₯ plus π.

As this line passes through the point π΄ with coordinates three, six, we can substitute these values into the equation to calculate π. Substituting in the coordinates gives us six is equal to minus three multiplied by three plus π. Minus three multiplied by three is equal to minus nine. Adding nine to both sides of this equation gives us a value of π equal to 15.

This means that the equation of π΄π· is π¦ equals minus three π₯ plus 15.