if a=1/3, b=2/5, c=(-1)/2 then 3a+5bc-30abc
Answers
Step-by-step explanation:
Median is the line joining the midpoint of one side of a triangle to the opposite vertex. So, the coordinates of D would be(
2
6+1
,
2
5+4
)::(
2
7
,
2
9
)
ii)
P divides AD in the ratio 2:1.
A(x
1
,y
1
)=(4,2), D(x
2
,y
2
)=(
2
7
,
2
9
)
m:n=2:1
Using section formula, we get the coordinates of P.
P(x,y)=(
m+n
nx
1
+mx
2
,
m+n
ny
1
+my
2
)
=
⎝
⎜
⎜
⎛
2+1
1⋅4+2⋅
2
7
,
2+1
1⋅2+2⋅
2
9
⎠
⎟
⎟
⎞
=(
3
11
,
3
11
)
iii)
Coordinates of E will be (
2
5
,3) and the coordinates of F=(5,
2
7
).
Coordinates of Q=(
m+n
nx
1
+mx
2
,
m+n
ny
1
+my
2
)
=
⎝
⎜
⎜
⎛
2+1
1⋅6+2⋅
2
5
,
2+1
1⋅5+2⋅3
⎠
⎟
⎟
⎞
=(
3
11
,
3
11
)
Coordinates of R=(
m+n
nx
1
+mx
2
,
m+n
ny
1
+my
2
)
=
⎝
⎜
⎜
⎛
2+1
1⋅1+2⋅5
,
2+1
1⋅4+2⋅
2
7
⎠
⎟
⎟
⎞
=(
3
11
,
3
11
)
iv)
The coordinates of P,Q and R are the same which is (
3
11
,
3
11
).
This point is called the centroid, denoted by G.
v)
Centroid of triangle ABC=(
3
x
1
+x
2
+x
3
,
3
y
1
+y
2
+y
3
)
solution
expand
Video Explanation
Solution to Question ID 465356
play-icon
Answer:The answer is 2
Step-by-step explanation:
Given, a=1/3, b=2/5, c=(-1)/2
Then, 3a+5bc-30abc = 3×1/3 + 5×2/5×(-1)/2 - 30×1/3×2/5×(-1)/2
= 1+(-1)-(-2)
= 2