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
