What is the length of segment XY? 4.5 units /45 units /53 units 9 units
2 answers:
Answer: The correct option is (C) √53 units.
Step-by-step explanation: We are given to find the length of the line segment XY in the graph.
We know that the length of a line segment is equal to the distance between its end points.
<u><em>DISTANCE FORMULA:</em></u> The distance between two points with co-ordiantes (a, b) ad (c, d) is given by
From the graph, we note that
the co-ordinates of the point X are (-4, 0) and the co-ordinates of the point Y are (3, 2).
Therefore, the distance between the points X and Y is given by
So, the length of the line segment XY is √53 units.
Option (C) is correct.
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Answer:
Therefore the value of x = 10 units
Step-by-step explanation:
Let label the Triangles first,
Δ ABC a right triangle at ∠ A =90°
Δ ADB andΔ ADC a right triangle at ∠ D =90°
Such that
AD = x
BD = 50
CD = 2
∴ BC = BD + DC = 50 + 2 = 52
To Find:
x = ?
Solution:
In right triangle By Pythagoras Theorem,
In right triangle Δ ADB andΔ ADC By Pythagoras Theorem we will have,
AB² = BD² + AD²
AB² = 50² + x² ..................equation ( 1 )
and
AC² = DC² + AD²
AC² = 2² + x² ...................equation ( 2 )
Now in right triangle Δ ABC,
BC² = AB² + AC²
Equating equation (1 ) and ( 2 ) and the given value we get
52² = 50² + x² + 2² + x²
∴ 2x² = 2704 - 2504
∴ 2x² =200
∴
Therefore the value of x = 10 units
