Answer:
12. √197
13. √89
14. 2√10
15. (-3, 2)
16. (3/2, 0)
17. (2, -8)
18. 21
Explanation:
12. Point 1: (-8, -2); Point 2: (6, -1)
d = √(x2 - x1)² + (y2 - y1)²
d = √(6 - (-8)² + (-1 - (-2)²
d = √(14)² + (1)²
d = √196 + 1
d = √197
13. Point 1: (-4, 5); Point 2: (4, 0)
d = √(x2 - x1)² + (y2 - y1)²
d = √(4 - (-4))² + (0 - 5)²
d = √(8)² + (-5)²
d= √64 + 25
d = √89
14. G: (-2, -3); H: (0, 3)
d = √(x2 - x1)² + (y2 - y1)²
d = √(0 - (-2))² + (3 - (-3))²
d = √(-2)² + (6)²
d = √4 + 36
d = √40
d = √4 x 10
d = 2√10
15. Point 1: (-1, -5); Point 2: (-5, 9)
Midpoint = ((x1 + x2))/2, ((y1 + y2))/2
Mid = (-1 + (-5)/2, (-5 + 9)/2
Mid = (-6)/2, (4)/2
Mid = (-3, 2)
16. Point 1: (7, -2); Point 2: (-4, 2)
Midpoint = ((x1 + x2))/2, ((y1 + y2))/2
Mid = (7 + (-4)/2, (-2 + 2)/2
Mid = (3)/2, (0)/2
Mid = (3/2, 0)
17. M:(-3, -1); Y:(-8, 6), X: (X, y)
Midpoint = ((x1 + x2))/2, ((y1 + y2))/2
X = ((-8 + x2)) ,((6 + y2))
÷ = -3 ÷ = -1
2 2
To get rid of the 2 multiply the 2 by -3 for X and -1 for Y
X = ((-8 + x2)) ,((6 + y2))
÷ = -3(2) ÷ = -1(2)
2(2) 2(2)
X = (-8 + x2) = -6, (6 + y2) = -2
+8 +8, -6 -6
X2 = 2, Y2 = -8
X: (2, -8)
18. QR = 8x - 51; RS = 3x - 6
8x - 51 = 3x - 6
-3x -3x
5x - 51 = -6
+ 51 +51
5x = 45
÷5 ÷5
x = 9
QR = 8(9) - 51
QR = 72 - 51
QR = 21
RS = 3x - 6
RS = 3(9) - 6
RS = 21
(QR + RS)/2
(21 + 21)/2
42/2 = 21
QS = 21
I really hope this helps!