Answer:
<em>AB = 5√2</em>
<em>AC = √145</em>
<em>BC = √65</em>
Step-by-step explanation:
Using the formula for calculating the distance between two points
D = √(x2-x1)²+(y2-y1)²
For AB A(-3,6),B(2,1),
AB = √(2+3)²+(1-6)²
AB = √(5)²+(-5)²
AB = √25+25
AB = √50
<em>AB = 5√2</em>
For AC A(-3,6) and C(9,5)
AC = √(9+3)²+(5-6)²
AC = √(12)²+(-1)²
AC = √144+1
<em>AC = √145</em>
For BC B(2,1), and C(9,5)
BC = √(9-2)²+(5-1)²
BC = √(7)²+(4)²
BC = √49+16
<em>BC = √65</em>
<em></em>
<em>Since All the sides are difference, hence triangle ABC is a scalene triangle</em>
The answer would be 42.875
what are the other answers
The dot product is used to determine the magnitude of the resultant vector of two component vectors. It is expressed as a·b. It does not literally mean that you multiply their values. Instead, you multiply their matrices. However, since we cannot find matrices, let's just find the resultant vector through theorems involving triangles. By cosine law:
R = √[a² + b² - 2abcos(3π/4)]
R = √[60² + 30² - 2*60*30*cos(3π/4)]
R = 83.94
Thus, a·b = 83.94
Since we have two sides that are twice as long as the third side, we can designate each side as follows:
First side of triangle: 2x
Second side of triangle: 2x
Third side of triangle: x
Since all three sides add up to equal 60, we can set up the following equation and solve for each side:
(x) + (2x) + (2x) = 60
5x = 60 --> x = 12
Side 1 length: 2x = 2(12) = 24
Side 2 length: 2x = 2(12) = 24
Side 3 length: x = 12
I hope this helps!!
