Geometry Concepts and Problem Solving

The video tutorial explains how to find the equation of the altitude from point P in triangle PQR. It begins by identifying the vertices of the triangle and then calculates the gradient of line QR. Using the property of perpendicular lines, the gradient of line PS is determined. Finally, the equation of line PS is derived using the point-slope form. The tutorial concludes with a call to action for viewers to subscribe to the channel.

What are the coordinates of point Q in the triangle PQR?

• (-4, 5)

• (2, -2)

• (4, 1)

• (0, 0)

Which line is the altitude from point P perpendicular to?

• Line QR

• Line PR

• Line RS

• Line PQ

What is the formula used to calculate the gradient of a line?

• (y2 - y1) / (x2 - x1)

• (y1 + y2) / (x1 + x2)

• (x1 + x2) / (y1 + y2)

• (x2 - x1) / (y2 - y1)

What is the gradient of line QR?

• 2

• 1/2

• 1

• -1/2

If the gradient of QR is 1/2, what is the gradient of PS?

• -2

• 2

• 1

• -1/2

What is the relationship between the gradients of two perpendicular lines?

• They are reciprocals

• Their product is 1

• Their product is -1

• They are equal

Which point is used to substitute into the equation for line PS?

• Point Q

• Point R

• Point P

• Point S

What is the equation form used to substitute point P?

• x = my + c

• y - b = m(x - a)

• ax + by = c

• y = mx + c

What is the value of 'a' when substituting point P into the equation?

• 2

• 5

• 0

• -4

What is the value of 'b' when substituting point P into the equation?

• 0

• 2

• 5

• -4