SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

ΔAMT ~ ΔAHE. In ΔAMT, AM = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(AM)/(HA) = 7/5`, then construct ΔAMT and ΔAHE.

ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm. ∠D = 30°, ∠N = 20°, `(HP)/(ED) = 4/5`, then construct ΔRHP and ∆NED.

ΔABC ~ ΔPBR, BC = 8 cm, AC = 10 cm, ∠B = 90°, `(BC)/(BR) = 5/4` then construct ∆ABC and ΔPBR.

The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x = ______.

The distance between points P(–1, 1) and Q(5, –7) is ______.

If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______.

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.