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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).

The vertices of the triangle are given as A(3, 8), B(-4, 2) and C(5, 1)
Here, we have
x₁ = 3,    y₁ = 8
x₂ = -4,    y₂ = 2
and    x₃ = 5,    y₃ = 1
Now, area of triangle ABC
$equals 1 half left square bracket straight x subscript 1 left parenthesis straight y subscript 2 minus straight y subscript 3 right parenthesis space plus straight x subscript 2 left parenthesis straight y subscript 3 minus straight y subscript 1 right parenthesis plus straight x subscript 3 left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis right square bracket equals 1 half left square bracket 3 left parenthesis 2 plus 1 right parenthesis plus left parenthesis negative 4 right parenthesis left parenthesis negative 1 minus 8 right parenthesis plus 5 left parenthesis 8 minus 2 right parenthesis right square bracket equals 1 half left square bracket left parenthesis 3 space straight x space 3 space plus space left parenthesis negative 4 right parenthesis left parenthesis negative 9 right parenthesis plus 5 left parenthesis 6 right parenthesis right square bracket equals 1 half left square bracket 9 plus 36 plus 30 right square bracket equals 1 half space straight x space 75 space equals space 37.5 space sq. space units.$

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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.

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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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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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

184.
Find the area of a triangle whose vertices are : (3, 8), (-4, 2) and (5, 1).