Straight Lines: The Knowledge Trivia Quiz

Answer: Shortest route through points (a) and (b)

For instance, if points (a) and (b) are found on the circumference of a circle, the straight line would be a chord or, perhaps, the diameter or even a line of infinite length which passes through both points (a) and (b). The shortest route from the first point to the second point will always be in a straight line. Any longer distance would most likely be curved.

Answer: y = mx + c

"y = mx + c" is a very useful equation in this field of mathematical study. It can tell us such things as the gradient of the line as well as where the line intercepts the y-axis.

Answer: 3

By using the important formula "y = mx + c" this all becomes clear. The gradient is indicated by the letter "m". In the equation given above, m = 3. Therefore, the gradient or slope of the line will be +3.

Answer: -3

The importance of the formula "y = mx + c" is illustrated in this example. The part of the equation which deals with what is called the y-intercept (point at which the line crosses the y-axis) is "+ c". In the example above, it is giving c as -3, and that would therefore be the y-intercept.

This also emphasises the importance of signs in mathematics. A good example of where people neglect the importance of signs is when working with square roots (surds). A depiction of this would be to ask what is the square root of 25? Many will say, duh, it is five. Well, this is only half correct, as, the square root of 25 can also be -5.

Answer: (y2 - y1) / (x2 - x1)

This is just emphasising that the gradient of a line can be determined by dividing the 'change in the value of the y-coordinates' by the 'change in the value of the x-coordinates'. This can be expressed in general terms, in physics for example, as the 'change in y' divided by the 'change in x'.

In science, the change in something is indicated by the Greek letter delta, which, is drawn as a triangle. Gradient = delta y / delta x. So to put this formula into practice, take the co-ordinates of the points at either end of a straight line as (2,4) and (3,8). Using (y2 - y1) / (x2 - x1), you can substitute the values of the co-ordinates to ascertain the slope. So, y2 = 8, y1 = 4, x2 = 3 and x1 = 2. So, your calculation should look like this: (8-4)/(3-2) = 4/1 = 4.

The gradient of a line is illustrated algebraically by the letter m. Therefore, m = 4.

Answer: ([(x1+x2) / 2] , [(y1+y2) / 2])

On the surface this equation looks quite complicated, however, the clue really is in the question! What the question is asking is how can you find the co-ordinate for the mid-point, (z). The mid-point is literally half way between two point and, therefore fractionally, this is written as 1/2. What is important in this fraction is the denominator which is 2. So, the correct answer will also have a denominator of 2.

The proof that ([(x1+x2) / 2] , [(y1+y2) / 2]) is correct is as follows: (x1+x2) x 1/2 = (x1+x2) / 2.

The same follows for the y-coordinate. To illustrate this, take point (x) to be (2,5) and point (y) to be (3,7). Simple substitution will leave the equation: ([(2+3) / 2] , [(5+7) / 2]). The rest is down to basic arithmetic [(5/2) , (12/2)].

The midpoint of the line (xy) would therefore be (2.5,6).

Answer: Tangent

In the geometry of circles, a tangent ALWAYS meets the radius of a circle at 90 degrees.
With regards to trigonometry, a tangent is defined as the magnitude of the opposite side of a triangle divided by the corresponding magnitude of the adjacent side of the same triangle. Furthermore on the topic of trigonometry, sine is defined as the value of the opposite side of a triangle divided by the corresponding value of the hypotenuse of the same triangle. Cosine is the value of the adjacent side divided by the hypotenuse side.
As an extra piece of information, a moment is a phenomenon used in physics to quantify motion which is moving in a clockwise and anticlockwise direction. It is said that an object is in equilibrium when the clockwise rotation (moment) is the same as the rotation (moment) in the anticlockwise direction.
A moment is calculated by multiplying the magnitude of the applied force and the perpendicular distance of the point of application of force to the pivot. Moments are measured in Nm (Newton metres).

Answer: False

False! The midpoint of a line is always found on the straight line itself. It makes sense really, it couldn't possibly be the midpoint of the line if it wasn't situated on it. If you use the equation ([(x1+x2) / 2] , [(y1+y2) / 2]), you will find that the co-ordinate for the midpoint will be somewhere on the straight line itself, regardless of gradient or magnitude.

Answer: Perpendicular

Perpendicular lines always meet at right angles to each other.

Parallel means two lines with the same gradient that will never meet, even with infinite length. Complementary and supplementary angles are the terms given for many angles which add together to make 90 degrees or 180 degrees respectively.

Answer: -1

If the first line has a gradient (m1) of 5, then, the line that is perpendicular to it has to have a gradient that is the negative reciprocal of the gradient of the known line. So, if m1 = 5, m2 will equal -1/5. To find the outcome of these two gradients, you multiply them together (m1 x m2), which in this case will be, 5 x -1/5. This equals -5/5 which works out as -1.

Thanks for taking the time to play this quiz, I hope that you have enjoyed it!