Question

the angles of the quadrilateral abcd are a(4;6);b(6;-4);c(-4;-2) and d(-2;4). show that its diagonals are equal.

Answer 1

To show that the diagonals of the quadrilateral ABDC are equal, we can calculate the lengths of both diagonals using the distance formula. Upon calculation, we find that both diagonals have a length of 8√2.

Step-by-step explanation:

To show that the diagonals of the quadrilateral ABDC are equal, we need to find the lengths of both diagonals and compare them. Let's start by finding the lengths of the diagonals.

Diagonal AC can be found using the distance formula:

d(AC) = √((x2-x1)2 + (y2-y1)2)

Substituting the coordinate values for points A and C:

d(AC) = √((-4-4)2 + (-2-6)2)

d(AC) = √(82 + (-8)2)

d(AC) = √(64 + 64)

d(AC) = √128

d(AC) = 8√2

Similarly, diagonal BD can be found:

d(BD) = √((x2-x1)2 + (y2-y1)2)

Substituting the coordinate values for points B and D:

d(BD) = √((6-(-2))2 + ((-4)-4)2)

d(BD) = √(82 + (-8)2)

d(BD) = √(64 + 64)

d(BD) = √128

d(BD) = 8√2

Therefore, we can see that both diagonals AC and BD are equal, as they both have a length of 8√2.