Question

answer all my three questions before 12.30 p. m.
I will mark your all answers as brainliest and follow you and thank all your answers
if you put irrelevant answers you will be reported ​

Answer 1

6

 Construct ΔABC that follows the given condition.

 Let the coordinates of the point B be $\sf{B(a,b)}$. Point D is the midpoint of $\sf{\overline{AB}}$.

$\sf{\implies D(\dfrac{a-3}{2} ,\dfrac{b+5}{2} )}$

$\sf{\implies \dfrac{a-3}{2} =5,\dfrac{b+5}{2} =1}$

$\sf{\implies a=7,b=-3}$

$\sf{\therefore B(7,-3)}$

 Now let the coordinates of the point C be $\sf{C(c,d)}$. Point F is the midpoint of $\sf{\overline{CA}}$.

$\sf{\implies F(\dfrac{c-3}{2} ,\dfrac{d+5}{2} )}$

$\sf{\implies \dfrac{c-3}{2} =-5,\dfrac{d+5}{2} =-1}$

$\sf{\implies c=-7, d=-3}$

$\sf{\therefore C(-7,-3)}$

 Point E is the midpoint of $\sf{\overline{BC}}$.

$\sf{\implies E(\dfrac{7-7}{2} ,\dfrac{-3-3}{2} )}$

$\sf{\therefore E(0,-3)}$

7

 The two diagonals of a parallelogram intersect at the midpoint.

 $\sf{(-7,-3),(15,8)}$ and $\sf{(5,10),(3,-5)}$ are two endpoints of each diagonal.

 Now, the midpoint of the two diagonals must equal.

$\sf{\implies (\dfrac{-7+15}{2} ,\dfrac{-3+8}{2} )\:equals\:(\dfrac{5+3}{2} ,\dfrac{10-5}{2}) }$

$\sf{\implies (\dfrac{8}{2} ,\dfrac{5}{2} )\:equals\:(\dfrac{8}{2} ,\dfrac{5}{2}) }$

$\sf{\implies (4 ,\dfrac{5}{2} )\:equals\:(4 ,\dfrac{5}{2}) }$

 Therefore, it is a parallelogram.

8

 In the big triangle

• $\sf{\overline{AB}=25}$
• $\sf{\overline{BC}=20}$
• $\sf{\overline{CA}=15}$

 It is related to the 3-4-5 triangle.

$\sf{\implies{15^2+20^2=25^2}}$

 According to the converse of the Pythagorean theorem, ΔABC is a right triangle, right-angled at ∠C.

∴θ+φ=90°

 ΔACD is also a right triangle since $\sf{9^2+12^2=15^2}$.

 ΔBCD is also a right triangle since $\sf{12^2+16^2=20^2}$.

Let's find the trigonometric values.

• $\sf{sin\:\alpha=\dfrac{12}{15} }$
• $\sf{cos\:\beta=\dfrac{16}{20} }$
• $\sf{tan\:\phi=\dfrac{16}{12} }$

Three trigonometric values are $\dfrac{4}{5}$, $\dfrac{4}{5}$, and $\dfrac{4}{3}$ respectively.