Geometry and Algebra

Question 1

Two lines are parallel. What is true about their slopes?

Accepted Answer

Their slopes are equal.

Question 2

How can you check whether three points lie on one line?

Accepted Answer

Find the slope from the first point to the second and from the first point to the third. If they are equal, the points lie on the same line.

Question 3

What is the midpoint useful for?

Accepted Answer

Finding the exact centre point of a line segment — for example the centre of a circle given two ends of a diameter.

Question 4

How does the textbook find the point P on AB with AP : PB = m : n?

Accepted Answer

AP is \frac{m}{m+n} of AB. Take \frac{m}{m+n} of the change in x and in y from A to B, and add these changes to the coordinates of A.

Question 5

What is the midpoint of the line joining (x_1, y_1) and (x_2, y_2)?

Accepted Answer

\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right): half the change in each coordinate is added to the first point.

Sample questions