information about cherry tree
Answers
Answer:
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Explanation:
We will proof the definition of section formula.
Section of a Line Segment
Let AB be a line segment joining the points A and B. Let P be any point on the line segment such that AP : PB = λ : 1
Section of a Line Segment
Then, we can say that P divides internally AB is the ratio λ : 1.
Note: If AP : PB = m : n then AP : PB =
m
n
: 1 (since m : n =
m
n
:
n
n
. So, any section by P can be expressed as AP : PB = λ : 1
Definition of section formula: The coordinates (x, y) of a point P divides the line segment joining A (x1, y1) and B (x2, y2) internally in the ratio m : n (i.e.,
AP
PB
=
m
n
) are given by
x = (
mx2+nx1
m+n
, y =
my2+ny1
m+n
)
Proof:
Let X’OX and YOY’ are the co-ordinate axes.
Let A (x1, y1) and B (x2, y2) be the end points of the given line segment AB.
Let P(x, y) be the point which divides AB in the ratio m : n.
Then,
AP
PB
=
m
n
)
We want to find the coordinates (x, y) of P.
Draw AL ⊥ OX; BM ⊥ OX; PN ⊥ OX; AR ⊥ PN; and PS ⊥ BM
AL = y1, OL = x1, BM = y2, OM = x2, PN = y and ON = x.
By geometry,
AR = LN = ON – OL = (x - x1);
PS = NM = OM – ON = (x2 - x);
PR = PN – RN = PN – AL = (y - y1)
BS = BM – SM = BM – PN = (y2 - y)
Clearly, we see that triangle ARP and triangle PSB are similar and, therefore, their sides are proportional.
Thus,
AP
PB
=
AR
PS
=
PR
BS
⟹
m
n
=
x−x1
x2−x
=
y−y1
y2−y
⟹
m
n
=
x−x1
x2−x
and
m
n
=
y−y1
y2−y
⟹ (m + n)x = (mx2 + nx1) and (m + n)y = (my2 + ny1)
⟹ x = (
mx2+nx1
m+n
and y =
my2+ny1
m+n
)
Therefore, the co-ordinates of P are (
mx2+nx1
m+n
,
my2+ny1
m+n
).
Answer:
A cherry is the fruit of many plants of the genus Prunus, and is a fleshy drupe (stone fruit).
Commercial cherries are obtained from cultivars of several species, such as the sweet Prunus avium and the sour Prunus cerasus. The name 'cherry' also refers to the cherry tree and its wood, and is sometimes applied to almonds and visually similar flowering trees in the genus Prunus, as in "ornamental cherry" or "cherry blossom". Wild cherry may refer to any of the cherry species growing outside cultivation, although Prunus avium is often referred to specifically by the name "wild cherry" in the British Isles.
Many cherries are allied to the subgenus Prunus subg. Cerasus, which is distinguished by having the flowers in small corymbs of several together (not singly, nor in racemes), and by having smooth fruit with only a weak groove along one side, or no groove. The subgenus is native to the temperate regions of the Northern Hemisphere, with two species in America, three in Europe, and the remainder in Asia. Other cherry fruits are borne on racemes and called bird cherries.