Question

Determine the coordinates of the vertices of the triangle to compute the area of the triangle using the distance formula (round to the nearest integer). FIRST GRAPH

A) 20 units^2
B) 30 units^2
C) 40 units^2
D) 50 units^2

Compute the perimeter of the rectangle using the distance formula. (round to the nearest integer) SECOND GRAPH
A) 33
B) 34
C) 38
D) 45

Answer 1

Answer: first one is D

Explanation:

Answer 2

1. D.
`50\text{ units}^2`

2. D. 45 units.

Explanation:

We have been two graphs.

1. To find the area of our given triangle we will use distance formula.

`\text{Distance}=√((x_2-x_1)^2+(y_2-y_1)^2)`

Upon substituting coordinates of base line of our triangle we will get,

`\text{Base length of triangle}=√((15-5)^2+(5-15)^2)`

`\text{Base length of triangle}=√((10)^2+(-10)^2)`

`\text{Base length of triangle}=√(100+100)`

`\text{Base length of triangle}=√(200)`

`\text{Base length of triangle}=10√(2)`

Now let us find the height of triangle similarly.

`\text{Height of triangle}=√((20-15)^2+(10-5)^2)`

`\text{Height of triangle}=√((5)^2+(5)^2)`

`\text{Height of triangle}=√(25+25)`

`\text{Height of triangle}=√(50)`

`\text{Height of triangle}=5√(2)`

`\text{Area of triangle}=\frac{\text{Base*Height}}{2}`

`\text{Area of triangle}=(10√(2)*5√(2))/(2)`

`\text{Area of triangle}=(50*2)/(2)`

`\text{Area of triangle}=50`

Therefore, area of our given triangle is 50 square units and option D is the correct choice.

2. Using distance formula we will find the length of large side of triangle as:

`\text{Large side of rectangle}=√((14-1)^2+(21-8)^2)`

`\text{Large side of rectangle}=√((13)^2+(13)^2)`

`\text{Large side of rectangle}=√(169+169)`

`\text{Large side of rectangle}=√(338)`

`\text{Large side of rectangle}=13√(2)`

`\text{Small side of rectangle}=√((4-1)^2+(5-8)^2)`

`\text{Small side of rectangle}=√((3)^2+(-3)^2)`

`\text{Small side of rectangle}=√(9+9)`

`\text{Small side of rectangle}=√(18)`

`\text{Small side of rectangle}=3√(2)`

`\text{Perimeter of rectangle}=2(\text{Length + Width)}`

`\text{Perimeter of rectangle}=2(13√(2)+3√(2)}`

`\text{Perimeter of rectangle}=2(16√(2)}`

`\text{Perimeter of rectangle}=32√(2)`

`\text{Perimeter of rectangle}=45.2548339959390416\approx 45`

Therefore, the perimeter of our given rectangle is 45 units and option D is the correct choice.