Question : What is the reflection of the point $(4,7)$ over the line $y=–1$?
Option 1: $(–6,7)$
Option 2: $(–4,–9)$
Option 3: $(4,–9)$
Option 4: $(–6,–7)$
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $(4,–9)$
Solution : Given: The point is $(4,7)$ and the line is $y=–1$. The formula for the reflection of the point $(x_1, y_1)$ over the line $ax+by+c=0$ is $\frac{x–x_1}{a}=\frac{y–y_1}{b}=\frac{–2(ax_1+by_1+c)}{a^2+b^2}$. Here, are the values of $a=0$, $b=1$, and $c=1$. $(x–4)=0$ and $(y–7)=\frac{–2(7+1)}{1}$ ⇒ $x=4$ and $y=–16+7$ ⇒ $x=4$ and $y=–9$ Hence, the correct answer is $(4,–9)$.
Candidates can download this e-book to give a boost to thier preparation.
Application | Eligibility | Admit Card | Answer Key | Preparation Tips | Result | Cutoff
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 $\left(3 y+\frac{3}{y}\right)=8$, then find the value of $\left(y^2+\frac{1}{y^2}\right)$.
Option 1: $5\frac{1}{9}$
Option 2: $4\frac{5}{6}$
Option 3: $7\frac{1}{9}$
Option 4: $9\frac{1}{9}$
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 : If $y$ is an integer, then $(y^{3}-y)$ is always multiple of _____.
Option 1: 5
Option 2: 7
Option 3: 9
Option 4: 6
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)
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile