The point of intersection of the duagonals of a parallelogram ABCD with vertices A(2,7) andC(-6,1) is: a.(-4,8) b.(-2,4)?

Question

Answer

The point of intersection=((2-6/2),(7+1)/2)=(-2,4)

Answer

The triangle formed by joining the points (0,0),(0,4),(3,4) in the same order is
a.Equilateral
b.Right angled
c.Isosceles
d obtuse angled

Answer

Point of Intersection of Diagonals of a Parallelogram

Given:

Parallelogram ABCD

Vertices A(2,7) and C(-6,1)

Step 1: Find the Midpoints of AC and BD

Let's first find the midpoint of AC:

x-coordinate of midpoint = (x₁ + x₂)/2 = (2 + (-6))/2 = -2

y-coordinate of midpoint = (y₁ + y₂)/2 = (7 + 1)/2 = 4

So, the midpoint of AC is (-2,4).

Similarly, let's find the midpoint of BD:

x-coordinate of midpoint = (x₃ + x₄)/2 = (?? + ??)/2 = ??

y-coordinate of midpoint = (y₃ + y₄)/2 = (?? + ??)/2 = ??

But we don't have the coordinates of points B and D. So, we need to find them first.

Step 2: Find the Coordinates of Point B and D

Recall that opposite sides of a parallelogram are parallel and equal in length.

So, we can find the coordinates of B and D by adding or subtracting the same vector from A and C, respectively.

Let's find the vector between A and C:

x-component of vector AC = x₂ - x₁ = -6 - 2 = -8

y-component of vector AC = y₂ - y₁ = 1 - 7 = -6

So, vector AC is (-8,-6).

Now, to find B, we add vector AC to A:

x-coordinate of B = x₁ + (-8) = 2 - 8 = -6

y-coordinate of B = y₁ + (-6) = 7 - 6 = 1

So, the coordinates of B are (-6,1).

Similarly, to find D, we subtract vector AC from C:

x-coordinate of D = x₃ - (-8) = ?? + 8 = ??

y-coordinate of D = y₃ - (-6) = ?? + 6 = ??

But we don't have the coordinates of point D yet. So, let's move to the next step.

Step 3: Find the

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