TRIGONOMETRY (Application of the Distance Formula)?

Question

1. Find x if the distance between (1,3) and (x,9) is 10

2. Find the area of the rectangle with vertices A (-5, 1), B (-3, -1), C (3, 5), and D (0, 3)

3. A quadrilateral is a rhombus if all four sides are equal in length. If P(1, 2), Q(4, -2), R(1,-6), and S are consecutive vertices of a rhombus, what are the coordinates of Point S

4. A Stringer is a board that supports a set of stairs. If a staircase is 8 ft. high and extends 10 ft. horizontally. Find the length of the stringer to the nearest foot.

Answer 1

these questions are not related to trigonometry, they are perhaps belong to the topic of coordinate geometry.

Answer 2

Question 1
(x - 1)² + (9 - 3)² = 100
(x - 1)² = 64
(x - 1) = ± 8
x = ±8 + 1
x = 9 , x = - 7

Question 2
AB² = 2² + 2²
AB² = 8
AB = 2.√2
BC² = 9 + 4
BC² = 13
BC = √13
Area = 2.√2 x √13 units²
Area = 2.√26 units²

Question 3
Using vectors:-
PR = (0 , - 8)
(1/2).PR = (0 , - 4)
OT = OP + (1/2)PR
OT = (1 , 2) + (0 , - 4)
OT = (1 , - 2)
OQ + QT = OT
QT = OT - OQ
QT = (1 , - 2) - (4 , - 2)
QT = (-3 , 0)
OS = OP + PQ + 2QT
OS = (1 , 2) + (3 ,- 4) + (- 6 , 0)
OS = (-2 ,- 2)
S(- 2 , -2)

Question 4
L² = 10² + 8²
L² = 164
L = 4 x 41
L = 2√41
L = 12.9 ft is length of stringer.

Answer 3

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Answer 4

1) by PYTHAGORAS
(x-1)^2 +(9-3)^2=100
so x^2 -2x-63=0
(x-9)(x+7)=0
so x=9 or x=-7

2) Take AB as height BC as width
AB= sqr(4+4) BC=sqr(36+36)
so area = sqr(8) * sqr(72) = sqr( 8*72) =24

3)midpoint PR is (0,-2) so thats the midpoint of QS
so S is (-4,2)

4)sqr(64+100) = 13