Mr. Smith works from 8:00 a.m. to 5:30 p.m. How many hours did Mr. Smith
work?
Answers
Answer:
★ CO – ORDINATE GEOMETRY FORMULAS —
I) Distance Formula
Distance formula is used to find the distance between two given Points.
{\underline{\boxed{\frak{Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}}}}
Distance=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
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II) Section Formula
Section Formula is used to find the ratio(x, y) of the point (A) Which divides the line segment joining the points (B) and (C) internally or externally.
{\underline{\boxed{\frak{ \Big(x, y \Big) = \Bigg(\dfrac{mx_2 + nx_1}{m + n} \dfrac{my_2 + ny_1}{m + n}\Bigg)}}}}
(x,y)=(
m+n
mx
2
+nx
1
m+n
my
2
+ny
1
)
⠀
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III) Mid – point Formula
Mid Point formula is used to find the Mid points(x, y) on any line segment.
{\underline{\boxed{\frak{\Bigg(\dfrac{x_1 + x_2}{2} \; or\; \dfrac{y_1 + y_2}{2} \Bigg)}}}}
(
2
x
1
+x
2
or
2
y
1
+y
2
)
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IV) Trisection of Line Formula
To find the points of trisection A and B which divides the line segment joining the points
\sf Q(x_1, y_1)Q(x
1
,y
1
) and \sf R (x_2, y_2)R(x
2
,y
2
) into three equal parts.
\underline{\boxed{\frak{A = \dfrac{x_2 + 2x_1}{3},\; \dfrac{y_2 + 2y_1}{3}\;\&\;B = \dfrac{2x_2 + x_1}{3},\; \dfrac{2y_2 + y_1}{3}}}}
A=
3
x
2
+2x
1
,
3
y
2
+2y
1
&B=
3
2x
2
+x
1
,
3
2y
2
+y
1
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V) Centroid of Triangle
If \sf A(x_1, y_1), B(x_2, y_2)A(x
1
,y
1
),B(x
2
,y
2
) and \sf C(x_3, y_3)C(x
3
,y
3
) are the vertices of any ∆ ABC, then the co–ordinates of its centroid (Q) are given by.
\underline{\boxed{\frak{Q = \dfrac{x_1 + x_2 + x_3}{3}, \: \dfrac{y_1 + y_2 + y_3}{3}}}}
Q=
3
x
1
+x
2
+x
3
,
3
y
1
+y
2
+y
3
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VI) Area of Triangle
If the points A, B and C are the vertices of a Δ ABC, then the formula of area of triangle is given by.
\underline{\boxed{\frak{\triangle = \dfrac{1}{2} x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}}}
△=
2
1
x
1
(y
2
−y
3
)+x
2
(y
3
−y
1
)+x
3
(y
1
−y
2
)
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Answer:
Answer is 9 hours and 30 minutes