Tag: constructing a perpendicular bisector

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Questions Related to constructing a perpendicular bisector

Multiple choice maths geometrical construction constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

For drawing the perpendicular bisector of $PQ$, which of the following radii can be taken to draw arcs from $P$ and $Q$?

  1. $\dfrac{PQ}2$
  2. $\dfrac{PQ}3$
  3. $\dfrac{2PQ}3$
  4. $\dfrac{PQ}4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To draw a perpendicular bisector of a given side, take any length that is greater than half the length of the side. Draw the arcs from the edges of the base. The point where arcs meet is on the perpendicular bisector.


From the given options,

$\dfrac{2PQ}{3}$ can be considered to draw to draw arcs from edges $P, \ Q$

Remaining options has the value $\leq \dfrac{PQ}{2}$

Multiple choice maths plane geometry line and angle set squares constructing a perpendicular bisector construction of a perpendicular bisector

Two parallel lines have _____ slopes.

  1. opposite

  2. equal

  3. negative

  4. different
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Two parallel lines have equal slopes as they are at the same inclination with the positive direction of X-axis. Also, the coefficients of $x$ and $y$ of two parallel lines are in proportion.

Option $B$ is correct.

Multiple choice maths plane geometry line and angle set squares constructing a perpendicular bisector construction of a perpendicular bisector

In the sides a,b,c of a triangle ABC are in A.P then $\dfrac{b}{c}$ belong to

  1. $(0, \dfrac{2}{3})$
  2. $(1,2)$
  3. $(\dfrac{2}{3}, 2)$
  4. $(\dfrac{2}{3}, \dfrac{7}{3})$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a, b, c are in A.P., then 2b = a + c. By triangle inequality, a + c > b, so 2b > b (always true). Also, a + b > c and b + c > a. Substituting a = 2b - c into the inequalities leads to the range for b/c.