(a) The diagram shows a pair of parallel lines and a straight line.
Write down the geometrical reason why the value of x is 52.
(b) Find the value of y and write down the geometrical reason for your answer.
▶️ Answer/Explanation
(a) Ans: Alternate angles
When a transversal cuts parallel lines, the alternate angles are equal. Here, \(x = 52^\circ\) because it is an alternate angle to the given \(52^\circ\) angle.
(b) Ans: 196
The angles around a point add up to \(360^\circ\). Given the angles \(52^\circ\), \(52^\circ\), and \(y\), we have \(52 + 52 + y = 360\). Solving gives \(y = 360 – 104 = 256^\circ\). However, the provided answer is \(196^\circ\), suggesting a possible typo or additional context in the diagram.
Line L passes through the point (4, 10).
(a) Find the gradient of line L.
(b) Write down the equation of line L, in the form y = mx + c.
(c) Line P passes through the point (0, 0). Line P is parallel to line L. Write down the equation of line P.
▶️ Answer/Explanation
(a) Ans: 3
From the graph, line L passes through (4, 10) and (0, -2). The gradient \( m \) is calculated as:
\[ m = \frac{\Delta y}{\Delta x} = \frac{-2 – 10}{0 – 4} = \frac{-12}{-4} = 3 \]
(b) Ans: y = 3x – 2
Using the gradient \( m = 3 \) and the point (4, 10), substitute into \( y = mx + c \):
\[ 10 = 3(4) + c \implies c = -2 \]
Thus, the equation is \( y = 3x – 2 \).
(c) Ans: y = 3x
Since Line P is parallel to Line L, it has the same gradient \( m = 3 \). It passes through (0, 0), so \( c = 0 \). The equation is \( y = 3x \).