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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).

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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.

Let co-ordinates of centre be 0(2α - 1,7), which passes through the point A(- 3, - 1).

Fig. 7.23(A)
Now OA = 10 units

$OA space equals space square root of left parenthesis 2 straight alpha minus 1 plus 3 right parenthesis squared plus left parenthesis 7 plus 1 right parenthesis squared end root 10 space equals space square root of 4 straight a squared plus 4 plus 8 straight alpha plus 64 end root$

Squaring
100 = 4α² + 8α + 68
4α² + 8α - 32 = 0
α² + 2α - 8 = 0
α² + 4α + 2α - 8 = 0
α(α + 4) + 2(α - 8) = 0
(α - 4) (α - 2) = 0
α = -4, α = 2.

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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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