SSC (English Medium) 10th Standard - Maharashtra State Board Important Questions

If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.

If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.

The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B.

AB and AC are the two chords of a circle whose radius is r. If p and q are
the distance of chord AB and CD, from the centre respectively and if
AB = 2AC then proove that 4q2 = p² + 3r².

Δ SHR ∼ Δ SVU. In Δ SHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and
SHSV = 53 then draw Δ SVU.

Distance of point (−3, 4) from the origin is ______.

From the given number line, find d(A, B):

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

Δ AMT ∼ ΔAHE. In  Δ AMT, MA = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(MA)/(HA) = 7/5`. construct  Δ AHE. 

Find the co-ordinates of the centroid of the Δ PQR, whose vertices are P(3, –5), Q(4, 3) and R(11, –4) 

Draw seg AB of length 9.7 cm. Take a point P on it such that A-P-B, AP = 3.5 cm. Construct a line MN ⊥ sag AB through point P.

∆ABC ∼ ∆AQR. `(AB)/(AQ) = 7/5`, then which of the following option is true?

Construct an equilateral ∆ABC with side 5 cm. ∆ABC ~ ∆LMN, ratio the corresponding sides of triangle is 6 : 7, then construct ΔLMN and ΔABC.

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

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(7, 5) and B(2, 5).

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

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

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)`

What is the distance of the point (– 5, 4) from the origin?