Question

Find the length of the midline KH in Trapezoid SQUAD.​

Answer 1

Question

• Find the length of the midline KH in Trapezoid SQUAD.

Answer

`\sf\red{the \: length \: of \: the \: middle \: kh \: is \: (a \: + \: b)/(2) units}`

• use the midpoint formula to find the coordinates of points K and H

`\begin{gathered}{\boxed{\begin{array}{cccc} \sf{For \: point \: K} & \\ & \sf \\ \sf{Q( 0, 0 )\: U( c, d )}\\ \tiny * = * ( * 1 \: + y \: 2)/(2) \: \: y = (y \: 1 + y \: 2)/(2) \\ \tiny{ * = (0 \: + \: c)/(2) \: y = (0 \: + \: d)/(2) } \\ \tiny{ * = (c)/(2) \: \: \: y = (d)/(2) } \\ \tiny \red{the \: coordinates \: of \: point \: K \: are \: ( (c)/(2) . (d)/(2) )} \end{array}}}\end{gathered}`

`\begin{gathered}{\boxed{\begin{array}{cccc} \sf{For \: point \: H} \\ \\ \tiny{b),d] D(a,0)} \\ \tiny * = ( * 1 * 2)/(2) \: \: y = (y \: 1 + y \: 2)/(2) & \\ \tiny{ * = (a + (c + b))/(2) \: \: y = (0 + d)/(2) } &\\ \tiny{ * = (a + b + c)/(2) \: \: \: y = (d)/(2) } \\ \tiny\red{ The\: coordinates\: of\: point \:H\: are ( (a + b + c)/(2) , (d)/(2) ) }\end{array}}}\end{gathered}`

• b. use the distance for mula to find the length of KH

`\sf \: k( (c)/(2) . (d)/(2) ) \: \: \: h( (a + b + c)/(2) . (d)/(2) )`

`\sf \: d = \sqrt{(x2 - * 1) {}^(2) + (y2 - y1) {}^(2) }`

`\sf \: kh = \sqrt{ ([a \: + \: b \: + \: c)/(2) - (c)/(2) {}^(2) + ( (d)/(2) - (d)/(2)) ^(2) }`

`\sf \: kh = \sqrt{ ((a + b)/(2)) {}^(2) + (0) {}^(2) }`

`\sf \: kh = \sqrt{( (a + b)/(2)) {}^(2) }`

`\sf \: kh = (a + b)/(2)`

Final Answer

`\sf\red{the \: length \: of \: the \: middle \: kh \: is \: (a \: + \: b)/(2) units}`