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03.02.2020 •
Mathematics
If the ends of the base of an isosceles triangle are at (2,0) & (0,1) & the eqn of one side is
x=2,
then the orthocentre of the triangle is
a) (3/2, 3/2)
b) (5/4, 1)
c) (3/4, 1)
d) (4/3, 7/12)
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Ответ:
The orthocenter of the triangle is
and option b is correct.
Step-by-step explanation:
The ends of the base of an isosceles triangle are at (2,0) & (0,1).
Orthocentre of the triangle is the intersection point of all three altitudes from its vertices.
First find any two altitudes, then find intersection point of altitudes.
The equation of a side is x=2, which is an vertical line. The opposite vertices of this side is (0,1), so the perpendicular line is a horizontal line. The equation of first altitude is
In an isosceles triangle, then attitude is the median of non-equal side. It means the altitude is passing through the midpoint of base side.
Slope of base side is
The product of slopes of two perpendicular lines is -1.
The point slope form of a line is
Where, m is slope.
The slope of second altitude is 2 and it passing through the pint (1,0.5), therefore the equation of second altitude is
From equation (1) and (2), we get
Therefore the orthocenter of the triangle is
and option b is correct.
Ответ:
15 ways
1 and 21 and 3 1 and 4 1 and 51 and 62 and 32 and 42 and 52 and 63 and 43 and 53 and 64 and 54 and 65 and 6Hope this helps