Please help me with acellus
1 answer:
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Answer:
The possible coordinates of point C are (4.5 , 5.5) OR (4.5 , 0.5)
Step-by-step explanation:
* <em>Lets explain how to solve the problem</em>
- The problems it seems that difficult but if you think about the
properties of the isosceles triangle
∵ AB is the hypotenuse of the right isosceles Δ ABC
∴ The equal sides are AC and BC
∵ A = (2 , 3) and B = (7 , 3)
- <u><em>The y-coordinates of A and B are equal then, AB is a horizontal</em></u>
<em> </em><u><em>segment</em></u>
∴ <u><em>The vertical segment drawn from point C to the hypotenuse AB </em></u>
<em> </em><u><em>will bisect it </em></u>
∴ <u><em>The x-coordinate of point c equal the x-coordinate of the mid-point</em></u>
<em> </em><u><em>of AB</em></u>
∵ The x-coordinate of the mid-point of AB is half the sum of
x-coordinates of points A and B
∴ The x-coordinate of point C is
∴ <em>The x-coordinate of point C is 4.5</em>
∴ C = (4.5 , y)
* <em>Now lets think about the slopes of the perpendicular lines</em>
- <u><em>The product of the slopes of the perpendicular line is -1</em></u>
∵ ΔABC is isosceles right triangle, where m∠C = 90°
∴ AC ⊥ BC
- <em>Lets find the slopes of AC and BC</em>
∵ A = (2 , 3) , B = (7 , 3) and C = (4.5 , y)
∵
∵
∵
∴
- By using cross multiplication
∴ (y - 3)² = - 2.5 × 2.5 × -1
∴ (y - 3)² = 6.25
- By taking √ for both sides
∴ y - 3 = ± 2.5
∴ y - 3 = 2.5 <em>OR </em> y - 3 = -2.5
∵ y - 3 = 2.5 ⇒ add 3 to both sides
∴ y = 5.5
<em>OR</em>
∵ y - 3 = -2.5 ⇒ add 3 to both sides
∴ y = 0.5
∴ <em>The y-coordinates of point C are 5.5 or 0.5</em>
* <em>The possible coordinates of point C are (4.5 , 5.5) OR (4.5 , 0.5) </em>