Answer:
Not sure what your unit of measurement is, so I'm using units
a. Line LM = 12 units; Line MN = 37 units; Line LN = 35 units
b. 84 units
c. 210 units
Explanation:
Distance Formula: √(x2 - x1)² + (y2 - y1)²; (where (x2, y2) is a point and (x1, x2) is another point)
a.
Line LM
= √(x2 - x1)² + (y2 - y1)²
= √(7 - 7)² + (16 - 4)²
= √(0)² + (12)²
= √ 144
= 12 (the previous step can be skipped by the square root and the squared canceling out)
Line MN
= √(x2 - x1)² + (y2 - y1)²
= √(42 - 7)² + (4 - 16)²
= √(35)² + (-12)²
= √1225 + 144
=√1369
= 37
Line LN
= √(x2 - x1)² + (y2 - y1)²
= √(42 - 7)² + (4 - 4)²
= √(35)² + (0)²
= √1225
= 35 (again, previous step can be skipped by canceling out)
b. Perimeter – add all the side lengths up
12+37+35
49+35
84
c. Area of Triangle – 1/2bh
*Note: Side LM is the base of the triangle, and Side LN is the height
1/2(12)(35)
1/2(420) **Can also be written as 420/2
210