Math, asked by shiv13am, 1 year ago

can A(3,4), B(0,-5) C(3,-1) be vertex of triangle?if your answer yes,find area of triangle .hence find length of altitude on segment BC

Answers

Answered by 2singhrashi
5

Answer: area = 1.5 sq. Cm ; altitude length = 3 cm

Step-by-step explanation:

If the slopes of the line connecting any two given points is equal to the slopes connecting other two given points, then the points are concurrent i.e., they lie on the same line and thus they cannot for a triangle

Let us find the slopes between the points using the formula

\frac{y^{2}-y^{1}}{x^{2}-x^{1}}

Where x1,y1 and x2,y2 are the coordinates of the given points

Slope of AB = \frac{3-0}{4-(-5)} = \frac{3}{9} = \frac{1}{3}

Slope of BC = \frac{3-0}{-1-(-5)} = \frac{3}{4}

Since slope of AB ≠ slope of BC

The given coordinates form a triangle

Area of the triangle is

\frac{1}{2} * | [ x1(y2-y3) + x2(y3-y1) + x3(y1-y3) ] |

Where x1,y1; x2,y2 and x3,y3 are the coordinates of the triangle

The modulus is applied to ensure that the area of the triangle is a positive value

Applying the formula and substituting the values, we get

\frac{1}{2} * | [ 3(-5-(-1)) + 0(-1-4) + 3(4-(-1)) ] |

Onsolving we get

Area = 3/2 = 1.5 cm

We now find the equation of the line BC

Formula to find the equation of a line if two points on the line is given is

\frac{y - y1}{x - x1} = \frac{x2 - x1}{y2 - y1}

Substituting the values of the coordinates of B and C

\frac{y - (-5)}{x - 0} = \frac{-1 -(-5)}{3 - 0}\\\\\frac{y+5}{x} = \frac{4}{3}\\\\(y+5) * 3 = 4x\\\\3y + 15 = 4x\\\\4x-3y-15=0

To find the length of the altitude from A to BC, we use the formula

\frac{| a*x1 + b*y1 + c |}{\sqrt{a^{2} +b^{2}}}

Where a*x1 + b*y1 + c is the equation with the coordinates from which the perpendicular distance is to be found is substituted in that equation

So, substituting the values and solving

\frac{| 4(3) - 3(4) - 15 |}{\sqrt{4^{2}+3^{2}}}\\\\\frac{15}{5}\\\\

Therefore the of the altitude from A to BC = 3 cm

Please brainlist my answer, if helpful!

Answered by kinjalshah8380
0

Answer:

Area=21∣∣∣∣∣∣∣∣−3014−11521∣∣∣∣∣∣∣∣

=21[−3(−1−2)−4(−2)+5(+1)]

=21[−3(−3)−4(−2)+5(1)]

=21[−3(−1−2)−4(−2)+5(+1)]

=21[−3(−3)−4(−2)+5(1)]

=21[9+8+5]

=11

BC=(5−4)2+(2+1)2

=1+9=10

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