Determine the locus of a point inside a square PQRS which is eqidistant from PQ and QR
The diagonal QS
the perpendicular bisector of PQ
The diagonal PR
side SR
Correct answer is A
The diagonal QS bisects the angle formed by PQ and QR
∴ [A]
Find the midpoint of the line joining P(-3, 5) and Q(5, -3).
(1, 1)
(2, 2)
(4, 4)
(4, -4)
Correct answer is A
\(Mid point = \frac{(x_1 + x_2)}{2} ; \frac{(y_1 + y_2)}{2}\\
= \frac{(-3 + 5)}{2} ; \frac{(5 - 3)}{2}\\
= \frac{2}{2} ; \frac{2}{2}\\
= (1, 1)\)
The sum of the interior angles of a pentagon is 6x + 6y. Find y in the terms of x
y = 90 - x
y = 150 - x
y = 60 - x
y = 120 -x
Correct answer is A
6x + 6y = (n - 2) 180
6x + 6y= (5 - 2) 180
6(x + y) = 3 * 180
x + y = (3 * 180)/6
x + y = 90o
y = 90 - x
Find the value of α2 + β2 if α + β = 2 and the distance between points (1, α) and (β, 1)is 3 units
14
3
5
11
Correct answer is D
\(PQ = \sqrt{(β - 1)^{2} + (1 - α)^{2}}\\
3 =\sqrt{(β^{2} -2β^{2} + 1 + 1 - 2α + α^{2})}\\
3 = \sqrt{(α^{2} + β^{2} - 2α + 2β + 2)}\\
3 = \sqrt{(α^{2} + β^{2} - 2(α + β) + 2)}\\
3 = \sqrt{(α^{2} + β^{2} - 2 * 2 + 2)}\\
3 = \sqrt{(α^{2} + β^{2} - 2)}\\
9 = (α^{2} + β^{2} - 2)\\
α^{2} + β^{2} = 9 + 2\\
α^{2} + β^{2} = 11\)
60o
120o
180o
30o
Correct answer is A
\( ARC\hspace{1mm}length = (\frac{\theta}{360})\times 2\pi r\\22=\frac{3x}{360}\times \left(2 \times(\frac{22}{7})\times(\frac{7}{1})\right)\\3x = 180\\x = \frac{180}{3}\\x = 60^{\circ}\)