SSC (English Medium) इयत्ता १० वी - Maharashtra State Board Question Bank Solutions

Find distance between point A(– 3, 4) and origin O

Find distance between point A(7, 5) and B(2, 5)

Find distance of point A(6, 8) from origin

Find distance between points O(0, 0) and B(– 5, 12)

Find distance between point Q(3, – 7) and point R(3, 3)

Solution: Suppose Q(x₁, y₁) and point R(x₂, y₂)

x₁ = 3, y₁ = – 7 and x₂ = 3, y₂ = 3

Using distance formula,

d(Q, R) = `sqrt(square)`

∴ d(Q, R) = `sqrt(square - 100)`

∴ d(Q, R) =  `sqrt(square)`

∴ d(Q, R) = `square`

Find distance between point A(–1, 1) and point B(5, –7):

Solution: Suppose A(x₁, y₁) and B(x₂, y₂)

x₁ = –1, y₁ = 1 and x₂ = 5, y₂ = – 7

Using distance formula,

d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

∴ d(A, B) = `sqrt(square +[(-7) + square]^2`

∴ d(A, B) = `sqrt(square)`

∴ d(A, B) = `square`

If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x

Find distance CD where C(– 3a, a), D(a, – 2a)

Show that the point (11, – 2) is equidistant from (4, – 3) and (6, 3)

If the point P (6, 7) divides the segment joining A(8, 9) and B(1, 2) in some ratio, find that ratio

Solution:

Point P divides segment AB in the ratio m: n.

A(8, 9) = (x₁, y₁), B(1, 2 ) = (x₂, y₂) and P(6, 7) = (x, y)

Using Section formula of internal division,

∴ 7 = `("m"(square) - "n"(9))/("m" + "n")`

∴ 7m + 7n = `square` + 9n

∴ 7m – `square` = 9n – `square`

∴ `square` = 2n

∴ `"m"/"n" = square`

Show that P(– 2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle

Show that the point (0, 9) is equidistant from the points (– 4, 1) and (4, 1)

Show that the points (0, –1), (8, 3), (6, 7) and (– 2, 3) are vertices of a rectangle.

Show that the points (2, 0), (– 2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason

Show that A(1, 2), (1, 6), C(1 + 2 `sqrt(3)`, 4) are vertices of a equilateral triangle

Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?

Using distance formula decide whether the points (4, 3), (5, 1), and (1, 9) are collinear or not.

If a and b are natural numbers and a > b If (a² + b²), (a² – b²) and 2ab are the sides of the triangle, then prove that the triangle is right-angled. Find out two Pythagorean triplets by taking suitable values of a and b.

Prove that, The areas of two triangles with the same height are in proportion to their corresponding bases. To prove this theorem start as follows:

1. Draw two triangles, give the names of all points, and show heights.
2. Write 'Given' and 'To prove' from the figure drawn.

Find distance between points P(– 5, – 7) and Q(0, 3).

By distance formula,

PQ = `sqrt(square + (y_2 - y_1)^2`

= `sqrt(square + square)`

= `sqrt(square + square)`

= `sqrt(square + square)`

= `sqrt(125)`

= `5sqrt(5)`