Question : The point $Q(a,b)$ is first reflected in the y-axis to $Q_1$ and $Q_1$ is reflected in the x-axis to $(-5,3)$. The coordinates of point $Q$ are:
Option 1: $(–5,–3)$
Option 2: $(5,3)$
Option 3: $(–5,3)$
Option 4: $(5,–3)$
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Correct Answer: $(5,–3)$
Solution : Given: $Q1$ is reflected over the x-axis to $(–5,3)$. $Q1$ = image of $Q(a,b)$ over Y-axis = $(–5,3)$ Image of $Q(a,b)$ over Y-axis = $(–(–5),–(3))$ Image of $Q(a,b)$ over Y-axis = $(5,–3)$ Hence, the correct answer is $(5,–3)$.
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Question : The point $R(a,b)$ is first reflected over the origin to $R_1$ and $R_1$ is reflected over the X-axis to (–4, 2). The coordinates of point $R$ are:
Option 1: (–4, –2)
Option 2: (–4, 2)
Option 3: (4, 2)
Option 4: (4, –2)
Question : If $X$ is 20% less than $Y$, then find the values of$\frac{Y–X}{Y}$ and $\frac{X}{X–Y}$.
Option 1: $\frac{1}{5}$ and $-4$
Option 2: $5$ and $-\frac{1}{4}$
Option 3: $\frac{2}{5}$ and $-\frac{5}{2}$
Option 4: $\frac{3}{5}$ and $-\frac{5}{3}$
Question : The point P is the midpoint of the segment AB. The coordinates of point P are (2, 1) and that of point A are (11, 5). The coordinates of point B are:
Option 1: (–7, –3)
Option 2: (6.5, 3)
Option 3: (7, 3)
Option 4: (–6.5, –3)
Question : If $x=5$ ; $y=6$ and $z=-11$, then the value of $x^{3}+y^{3}+z^{3}$ is:
Option 1: –890
Option 2: –970
Option 3: –870
Option 4: –990
Question : Simplify the given expression and find the value for $x=-1$. $\frac{10 x^2+5 x+2 x y+y}{5 x+y}$
Option 1: –1
Option 2: 0
Option 3: 1
Option 4: 2
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