Answer to Question #132532 in Geometry for Mark

Question

If RS=44 and QS=68, Find QR

Find the distance between the point (1,4) and (-2,-1)

Find the midpoint of segment with endpoints (9,8) and (3,5)

ABC is right Triangle AB =

Find the distance between the points (1,-8)and(-7,-2)

Answer 1

If RS=44 and QS=68, Find QR

1. Line QS is a continuation of line RS: $QR = QS + QR = 68 + 44 = 112$
2. Point R belongs to line QS: $QR = QS - RS = 68 - 44 = 24$

Find the distance between the point (1,4) and (-2,-1):

Distance =$\sqrt{( -2 - 1)^2 + (-1 - 4)^2} = \sqrt{(-3)^2 + (-5)^2} = \sqrt{(9 + 25)} = \sqrt{34}$

Find the midpoint of segment with endpoints (9,8) and (3,5):

Midpoint(x_c, y_c):

$x_c = \dfrac{x_a + x_b}{2} = \dfrac{9 + 3}{2} = \dfrac{12}{2} = 6 , y_c = \dfrac{y_a + y_b}{2} = \dfrac{5 + 8}{2} = \dfrac{13}{2} = 6.5$

Midpoint(6, 6.5)

ABC is right Triangle AB =

Pythagorean theorem $AB = \sqrt{BC^2 + AC^2}$ $( if \angleС = 90\degree)$

Find the distance between the points (1,-8)and(-7,-2):

Distance =$\sqrt{( -7 - 1)^2 + (-2 - (-8))^2} = \sqrt{(-8)^2 + (-2 + 8)^2} = \sqrt{(-8)^2 + (6)^2} = \sqrt{(64 + 36)} = \sqrt{100} = 10$