Question

11. Show that points A, B and C are collinear by plotting the points in a
certain plane A(-1,2), B(2, -1) and C14.-3).
(Hint: Plot these points and show that they lie on the same straight lihel
( Show that the quadrilateral which have the vertices (1, 2), (2, 5).
(5,7),(4.4) is a parallelogram.
[Hint: Show that each pair of opposite sides of quadrilateral is equal.
then it is a parallelogram
​

Answer 1

Answer:

Ploted on the graph , quadrilateral is a parallelogram

Step-by-step explanation:

consider A(1,2) B(2,5) C (5,7) D(4,4)

show that AB = CD

AB = √((x₂-x₁)² + (y₂-y₁)²) = √((2-1)² + (5-2)²) = √(1+9) = √10

CD = √((x₂-x₁)² + (y₂-y₁)²) = √((4-5)² + (4-7)²) = √(1+9) = √10

so AB = CD

now AD = BC

AD = √((x₂-x₁)² + (y₂-y₁)²) = √((4-1)² + (4-2)²) = √(9+4) = √13

BC = √((x₂-x₁)² + (y₂-y₁)²) = √((5-2)² + (7-5)²) = √(9+4) = √13

so AD = BC

the quadrilateral  formed with those points is a parallelogram