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The points A(-3, 2) and B(1,4) are vertices of an isosceles triangle ABC, where angle B = 90°

(0) Find the length of the line AB.

(ii) Find the equation of the line BC.

User Rrichter
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1 Answer

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Answer:

Length of AB = 4.4721

Equation of line BC: y = -2x + 6

Explanation:

To find the length of the line AB, we just need to find the distance between the points A and B.

We can find distance with the equation:


distance = √((x_A - x_B)^2 + (y_A - y_B)^2)


distance = √((-3 - 1)^2 + (2 - 4)^2)


distance = 4.4721

To find the equation of the line BC, first let's find the slope of the line AB.

This slope is given by:


m_(AB) = ( y_A - y_B )/( x_A - x_B )


m_(AB) = ( 2 - 4 )/( -3 - 1) = (1)/(2)

The line AB is perpendicular to the line BC (because mB = 90°), so the slope of line BC is:


m_(BC) = -(1)/(m_(AB)) = -2

so the line BC is:


y = -2x + b

To find the value of b, we can use the point B (1,4):


4 = -2 + b


b = 6

So we have:


y = -2x + 6

User Mesilliac
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