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MATH / In the figure shown, a perpendicular segment is drawn from B in rectangle ABCD…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

In the figure shown, a perpendicular segment is drawn from B in rectangle ABCD to meet diagonal AC at point X. Side AB is 6 cm and diagonal AC is 10 cm. How many centimeters away is point X from the midpoint M of the diagonal AC? Express your answer as a decimal to the nearest tenth. [asy] draw((0,0)--(25,0)--(25,15)--(0,15)--cycle,linewidth(1)); draw((0,0)--(25,15),linewidth(1)); draw((7.2,4.3)--(0,15),linewidth(1)); dot((12.5,7.5)); label("MM",(12.5,7.5),N); label("AA",(0,0),S); label("BB",(0,15),N); label("CC",(25,15),N); label("DD",(25,0),S); label("XX",(7.2,4.3),SE); [/asy]
Plain-text mathematical notation (without MathML)
In the figure shown, a perpendicular segment is drawn from B in rectangle ABCD to meet diagonal AC at point X.  Side AB is 6 cm and diagonal AC is 10 cm.  How many centimeters away is point X from the midpoint M of the diagonal AC?  Express your answer as a decimal to the nearest tenth.

[asy]
draw((0,0)--(25,0)--(25,15)--(0,15)--cycle,linewidth(1));
draw((0,0)--(25,15),linewidth(1));
draw((7.2,4.3)--(0,15),linewidth(1));
dot((12.5,7.5));
label("M",(12.5,7.5),N);
label("A",(0,0),S);
label("B",(0,15),N);
label("C",(25,15),N);
label("D",(25,0),S);
label("X",(7.2,4.3),SE);
[/asy]
Original LaTeX notation
In the figure shown, a perpendicular segment is drawn from B in rectangle ABCD to meet diagonal AC at point X.  Side AB is 6 cm and diagonal AC is 10 cm.  How many centimeters away is point X from the midpoint M of the diagonal AC?  Express your answer as a decimal to the nearest tenth.

[asy]
draw((0,0)--(25,0)--(25,15)--(0,15)--cycle,linewidth(1));
draw((0,0)--(25,15),linewidth(1));
draw((7.2,4.3)--(0,15),linewidth(1));
dot((12.5,7.5));
label("$M$",(12.5,7.5),N);
label("$A$",(0,0),S);
label("$B$",(0,15),N);
label("$C$",(25,15),N);
label("$D$",(25,0),S);
label("$X$",(7.2,4.3),SE);
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
c94f6f78-0a64-558a-bec9-a3b4c9797fc6
task_key
geometry--test--c94f6f78-0a64-558a-bec9-a3b4c9797fc6
task_revision_id
1
config / split
geometry / test

Official source

initial import