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Coordinate Geometry

Short Answer Type

181. In what ratio does the point (-4, 6) divide the line segment joining the points A(-6, 10) and B(3, -8).

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182. Find the area of triangle whose vertices are (1, -1), (-4, 6) and (-3, -5).

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183. Find the area of the triangle formed by the points P(-1.5, 3), Q(6, -2) and R(-3, 4).

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184.

Find the area of a triangle whose vertices are : (3, 8), (-4, 2) and (5, 1).

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185. Find the area of a triangle formed by the points A(5, 2), B(4, 7) and C(7, -4).

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186. Find the area of the triangle formed by the points (0, 0), (6, 0) and (4, 3).

Let the vertices of the triangle are A(0, 0), B(6,0) and C(4, 3).

Here, we have
x₁ = 0,    y₁ = 0
x₂ = 6,    y₂ = 0
and    x₃ = 4, y₃ = 3
Now, Area of ∆ABC

$equals 1 half left square bracket straight x subscript 1 left parenthesis straight y subscript 2 minus straight y subscript 3 right parenthesis plus straight x subscript 2 left parenthesis straight y subscript 3 minus straight y subscript 1 right parenthesis plus straight x subscript 3 left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis right square bracket equals space 1 half left square bracket 0 left parenthesis 0 minus 3 right parenthesis plus 6 left parenthesis 3 minus 0 right parenthesis plus 4 left parenthesis 0 minus 0 right parenthesis right square bracket equals 1 half left square bracket 0 space straight x space minus 3 space plus space 6 space straight x space 3 space plus space 4 space straight x space 0 right square bracket equals 1 half left parenthesis 18 right parenthesis space equals space 9 space sq. space units.$

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187. One end of a diameter of a circle is at (2,3) and the centre is (-2, 5), what are the coordinates of the other end of his diameter?

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188. The centre of a circle is (2α - 1, 7) and it passes through the point (- 3, - 1). If the diameter of the circle is 20 units, then find the value(s) of α.

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189. If the mid-point of the line segment joining the points P(6, 6 - 2) and Q(- 2, 4) is (2, - 3), find the value of b.

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190. Do the points (8, 4), (5, 7) and (-1, 1) form a triangle ? If so, name the type of triangle formed.

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