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
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
Where x1,y1 and x2,y2 are the coordinates of the given points
Slope of AB =
Slope of BC =
Since slope of AB ≠ slope of BC
The given coordinates form a triangle
Area of the triangle is
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
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
Substituting the values of the coordinates of B and C
To find the length of the altitude from A to BC, we use the formula
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
Therefore the of the altitude from A to BC = 3 cm
Please brainlist my answer, if helpful!
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