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2. Show that diagonals of quadrilateral CUTE are congruent for C(5,-1), U(9,-1), T(9,0) and E(5.0). ​

2 Show That Diagonals Of Quadrilateral CUTE Are Congruent For C51 U91 T90 And E50 class=

Sagot :

Momomo6idn

Answer:

Swipe the pictures to see problem 1

Problem 1:

Find the length of each side of ∆EXP and ∆ABC

a. E(-3,-2), X(1,-1), P(0,2)

For E(-3,-2), X(1,-1)

use distance formula to get the length of each side

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (1 - (-3))² + (-1 - (-2))²

d² = (4²) + (1)²

d² = 16 + 1

d² = 17

d = √17

d = 4.123

For X(1,-1), P(0,2)

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (0 - 1)² + (2 - (-1))²

d² = (-1) ² + (3)²

d² = 1 + 9

d² = 10

d = √10

d = 3.162

For E(-3,-2), P(0,2)

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (0 - (-3))² + (2 - (-2))²

d² = (3) ² + (4)²

d² = 9 + 16

d² = 25

d = √25

d = 5

b.A(0,8), B(9,6), C(8,10)

For A(0,8), B(9,6)

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (9 - 0)² + (6 - 8)²

d² = (9)² + (-2)²

d² = 81 + 4

d² = 85

d = √85

d = 9.2195

For B(9,6), C(8,10)

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (8 - 9)² + (10 - 6)²

d² = (-1)² + (4)²

d² = 1 + 16

d² = 17

d = √17

d = 4.123

For A(0,8), C(8,10)

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (8 - 0)² + (10 - 8)²

d² = (8)² + (2)²

d² = 64 + 4

d² = 68

d = √68

d = 8.246

Please see attached file for the figure

Problem 2:

Show that ∆LIT is an isosceles right triangle, L(1,-3), I(1,5) and T(9,-3)

Isoscesles triangle is a triangle with 2 sides having equal lengths.

For L(1,-3), I(1,5)

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (1 - 1)² + (5 - (-3)²

d² = (0)² + (8)²

d² = 0 + 64

d² = 64

d = √64

d = 8

For I(1,5), T(9,-3)

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (9 - 1)² + (-3 - 5)²

d² = (8)² + (-8)²

d² = 64 + 64

d² = 128

d = √128

d = 11.3137

For L(1,-3) T(9,-3)

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (9 - 1)² + (-3 - (-3))²

d² = (8)² + (0)²

d² = 64 + 0

d² = 64

d = √64

d = 8

LI = 8, LT = 8, IT = 11.3137

LI and LT have equal sides, therefore, ∆LIT is an isosceles right triangle

Please see attached file for the figure

Problem 3:

Show that the diagonals of rectangle CUTE are congruent for C(5,1), U(9,-1), T(9,0) and E(5,0).

For C(5,1), U(9,-1)

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (9 - 5)² + (-1 - 1)²

d² = (4)² + (2)²

d² = 16 + 4

d² = 20

d = √20

d = 4.47

For T(9,0) and E(5,0)

d² = (x₂ - x₁)² + (y₂ - y₁)²

d² = (5 - 9)² + (0 - 0)²

d² = (-4)² + (0)²

d² = 16 + 0

d² = 16

d = √16

d = 4

The diagonals of the rectangle is NOT congruent because diagonal CU ≠ diagonal TE

View image Momomo6
View image Momomo6
View image Momomo6
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